The following articles will soon be published in this journal. Their publication status can be :
Department of Mathematics University of Bucharest 14 Academiei Street RO-010014 Bucharest Romania Simion Stoilow Institute of Mathematics of the Romanian Academy P.O. Box 1-764 RO-014700 Bucharest Romania Simion Stoilow Institute of Mathematics of the Romanian Academy P.O. Box 1-764 RO-014700 Bucharest Romania
Abstract: Given a prime number $p$ and $x$ an element of the Tate field $\mathbb{C}_p$, the main goal of the present paper is to provide an explicit generating set, which is given by the trace function of $x$ and all its derivatives, for the $\mathbb{C}_p$-Banach algebra of the Galois equivariant Krasner analytic functions defined on the complement in $\mathbb{P}^1(\mathbb{C}_p)$ of the orbit of $x$ with values in $\mathbb{C}_p$.
received 26.09.2017, accepted 13.03.2018 (14 pages)Mathematics Yildiz Technical University 34210, Istanbul Turkey
Abstract: In this study we first define the concept of Nadler type contraction in the setting of $H$-cone $b$-metric space with respect to cone $b$-metric spaces over Banach algebras. Next we prove the Banach contraction principle for such contractions by means of the notion of spectral radius and a solid cone in underlying Banach algebra. Finally we observe that the main result achieved in this work extends and generalizes the well known results associated with contractions of Nadler type.
received 05.02.2018, accepted 12.03.2018 (10 pages)Institut prÇparatoire aux Çtudes d ingÇnieurs de Nabeul UniversitÇ de Carthage Campus Universitaire Merazka, 8000 Nabeul Tunisie hatem_iaaoui@yahoo.com DÇpartement des MathÇmatiques FacultÇ des sciences de Tunis UniversitÇ Tunis El Manar naoufelbattikh@yahoo.fr
Abstract: The algebra of noncommutative differential forms has been defined by A. Connes in }$\left[ 4\right] .$ Using this algebra, M. Karoubi has defined cyclic homology and Hochschild homology groups (see. $\left[ 13\right] $). These groups are related to the algebraic K-theory. The purpose of this paper is to provide the noncommutative differential forms algebra with the structure of Gerstenhaber-Voronov algebras.
received 13.06.2017, accepted 01.03.2018 (15 pages)School of Mathematical Sciences Queen Mary University of London Mile End Road London E1 4NS England b.a.f.wehrfritz@qmul.ac.uk
Abstract: If $\{\gamma^{s+1}G\}$ and $\{\zeta_s(G)\}$ denote respectively the lower and upper central series of the group $G$, $s\ge 0$ an integer, and if $\gamma^{s+1}G/(\gamma^{s+1}G\cap\zeta_s(G))$ is polycyclic (resp. polycyclic-by-finite) for some $s$, then we prove that $G/\zeta_{2s}(G)$ is polycyclic (resp. polycyclic-by-finite). The corresponding result with polycyclic replaced by finite was proved in 2009 by G. A. Fern†ndez-Alcober and M. Morigi. We also present an alternative approach to the latter.
received 25.08.2017, accepted 23.02.2018 (10 pages)Universidade Federal de Viáosa Departamento de Fisica Av. Peter Henry Rolfs s/n Campus Universitario Viáosa, MG Brasil, CEP: 36.570-900 daniel.franco@ufv.br universidade Federal de Juiz de Flora Departamento de Matematica Campus Universitario Bairro Martelos Juiz de Flora, MG Brasil, CEP: 36.036-900 magno_branco@yahoo.com.br
Abstract: We address in this paper the issue of singularities of ultrahyperfunctions. Following the Carmichael's approach for ultrahyperfunctions, we study the relation between the singular spectrum of a class of tempered ultrahyperfunctions corresponding to proper convex cones and their expressions as boundary values of holomorphic functions. In passing, a simple version of the celebrated edge of the wedge theorem for this setting is derived from the integral representation without using cohomology.
received 18.08.2017, accepted 09.02.2018 (17 pages)Department of Mathematics and Statistics Youngstown State University One University Plaza Youngstown, OH 44555 United States
Abstract: A finite group $G$ is said to be \textsl{twisted cyclic} if there exist $\phi \in \text{Aut}(G)$ and $x \in G$ such that $G=\{(x^i)\phi^j\ :\ i,j \in \mathbb{Z}\}$. In this note, we classify all groups satisfying this property and determine that, if a finite group $G$ is twisted cyclic, then $G$ is isomorphic to $\mathbb{Z}_{p^n}$, $\mathbb{Z}_p\times \mathbb{Z}_p \times \cdots \times \mathbb{Z}_p$, $Q_8$, $\mathbb{Z}_{p^n}\times \mathbb{Z}_{p^n}$ or direct products of these groups for some prime $p$ and some $n\in \mathbb{Z}^{+}$.
received 03.01.2018, accepted 09.02.2018 (9 pages)IAZ - Lehrstuhl fÅr Algebra UniversitÑt Stuttgart Pfaffenwaldring 57 D-70569 Stuttgart Germany meinolf.geck@mathematik.uni-stuttgart.de
Abstract: Let $G(q)$ be a Chevalley group over a finite field $\F_q$. By Lusztig's and Shoji's work, the problem of computing the values of the unipotent characters of $G(q)$ is solved, in principle, by the theory of character sheaves; one issue in this solution is the determination of certain scalars relating two types of class functions on $G(q)$. We show that this issue can be reduced to the case where $q$ is a prime, which opens the way to use computer algebra methods. Here, and in a sequel to this article, we use this approach to solve a number of cases in groups of exceptional type which seemed hitherto out of reach.
received 24/01/2018, accepted 06.02.2018 (20 pages)Institute of Mathematics University of Bialystok K. Ciolkowskiego 1M 15-245 Bialystok Poland
Abstract: A subset $X$ of a finite group $G$ is called g-independent if there is no proper subset $Y$ of $X$ such that $\langle Y,\Phi(G) \rangle = \langle X,\Phi(G) \rangle.$ The group $G$ has the embedding property if every g-independent subset of $G$ can be embedded in a minimal generating set of $G$. If $X$ is a set of prime power order elements, then we say that $G$ has the pp-embedding property. In this note we classify all finite solvable groups with the pp-embedding property. Moreover we prove that this class is equal to the class of finite solvable groups with the embedding property.
received 26.10.2017, accepted 19.01.2018 (11 pages)Department of Applied Mathematics Northwestern Polytechnical University Xian China
Abstract: See the article
received 18.03.2017, accepted 09.12.2017 (32 pages)Hu, Huang School of Mathematics and Statistics Jiangsu Normal University Xuzhou, 221116 P. R. China Skiba Department of Mathematics Francisk Skorina Gomel State University Gomel 246019 Belarus
Abstract: see the article
received 26.02.2017, accepted 29.11.2017 (14 pages)Department of Mathematics Indian Institute of Technology Bombay Powai Mumbai 400 076 India
Abstract: In this paper we show that a large class of one-dimensional Cohen-Macaulay local rings $(A,\mathfrak{m})$ has the property that if $M$ is a maximal Cohen-Macaulay $A$-module then the Hilbert function of $M$ (with respect to $\mathfrak{m}$) is non-decreasing. Examples include
(1) Complete intersections $A = Q/(f,g)$ where $(Q,\mathfrak{n})$ is regular local of dimension three and $f \in \mathfrak{n}^2 \setminus \mathfrak{n}^3$.
(2) One dimensional Cohen-Macaulay quotients of a two dimensional Cohen-Macaulay local ring with pseudo-rational singularity.
2 Amner Road London SW11 6AA UK
Abstract: We show that if $\chi$ is an irreducible complex character of a metabelian $p$ - group $P,$ where $p$ is an odd prime, and if $x\in P$ satisfies $\chi(x)\neq 0$, then the order of $x$ divides $|P|/\chi(1)^2.$
received 21.06.2017, accepted 09.11.2017 (9 pages)Department of Mathematics Azarbaijan Shahid Madani University Tabriz Iran Department of Mathematics Razi University Kermanshah Iran
Abstract: In this paper, we give a characterization for Cohen--Macaulay rings $R/I$ where $I\subset R=K[y_1, \dots, y_n]$ is a monomial ideal which satisfies $\rm{bigsize}\, I=\rm{size}\, I$. Next, we let $S=K[x_1,\ldots,x_m, y_1,\ldots,y_n]$ be a polynomial ring and $I\subset S$ a monomial ideal. We study the sequentially Cohen-Macaulayness of $S/I$ with respect to $Q=(y_1,\ldots,y_n)$. Moreover, if $I\subset R$ is a monomial ideal such that the associated prime ideals of $I$ are in pairwise disjoint sets of variables, a classification of $R/I$ to be sequentially Cohen-Macaulay is given. Finally, we compute $\rm{grade}\,(Q, M)$ where $M$ is a sequentially Cohen-Macaulay $S$-module with respect to $Q$.
received 02.04.2017, accepted 23.10.2017 (14 pages)School of Mathematics Jilin University No. 2699 Qianjin Street Changchun China
Abstract: In this note, we extend the concept of $\Pi$-property of subgroups of finite groups and generalize some recent results. In particular, we generalize the main results of Li et al. [8] and Miao et al. [9].
received 28.08.2017, accepted 23.10.2017 (17 pages)Department of Mathematics North-Eastern Hill University Shillong-793022 India Department of Basic Sciences & Social Sciences North-Eastern Hill University Shillong-793022 India
Abstract: For each pair of integers $n=\prod_{i=1}^{r}p_i^{e_i}$ and $k \geq 2$, a digraph $G(n,k)$ is one with vertex set $\{0,1,\ldots ,n-1\}$ and for which there exists a directed edge from $x$ to $y$ if $x^k \equiv y \pmod n$. Using the Chinese Remainder Theorem, the digraph $G(n,k)$ can be written as a direct product of digraphs $G(p_i^{e_i},k)$ for all $i$ such that $1 \leq i \leq r$. A fundamental constituent $G_{P}^{*}(n,k)$, where $P \subseteq Q=\{p_1,p_2,\ldots,p_r\}$, is a subdigraph of $G(n,k)$ induced on the set of vertices which are multiples of $\prod_{{p_i} \in P}p_i$ and are relatively prime to all primes $p_j \in Q \smallsetminus P$. In this paper, we investigate the uniqueness of the factorization of trees attached to cycle vertices of the type $0$, $1$, and $(1,0)$, and in general, the uniqueness of $G(n,k)$. Moreover, we provide a necessary and sufficient condition for the isomorphism of the fundamental constituents $G_{P}^{*}(n,k_1)$ and $G_{P}^{*}(n,k_2)$ of $G(n,k_1)$ and $G(n,k_2)$ respectively for $k_1 \neq k_2$.
received 01.06.2017, accepted 20.10.2017 (28 pages)Université Claude Bernard Lyon 1 CNRS UMR 5208 Institut Camille Jordan 43 Blvd. du 11 novembre 1918 F-69622 Villeurbane cedex France
Abstract: Let $K$ be a discretly henselian field whose residue field is separably closed. Answering a question raised by G. Prasad, we show that a semisimple $K$-group $G$ is quasi-split if and only if it quasi-splits after a finite tamely ramified extension of $K$.
received 07.07.2017, accepted 16.10.2017 (9 pages)Institut de Mathématiques de Toulouse UMR5219, Université de Toulouse CNRS, UPS IMT F-31062 Toulouse Cedex 9 France
Abstract: We prove an equivalence of categories from formal complex structures with formal holomorphic maps to homotopy algebras over a simple operad with its associated homotopy morphisms. We extend this equivalence to complex manifolds. A complex structure on a smooth manifold corresponds in this way to a family of algebras indexed by the points of the manifold.
received 24.03.2017, accepted 25.09.2017 (38 pages)University of Stralsund Zur Schwedenschanze 15 18435 Stralsund Germany
Abstract: Let $A$ and $B$ be rational groups, i.e. torsion-free groups of rank-1 and thus subgroups of the rational numbers. This paper gives a short overview of the structure of $\text{Ext}\,(A,B)$ especially considering some interesting classes of torsion-free pairs.
received 06.03.2017, accepted 20.09.2017 (5 pages)Institut de Recherche Mathématique Avancée CNRS _ Université de Strasbourg 7 Rue René Descartes 67084 Strasbourg CEDEX France
Abstract: Motivated by the Beauville--Voisin conjecture about Chow rings of powers of $K3$ surfaces, we consider a similar conjecture for Chow rings of powers of EPW sextics. We prove part of this conjecture for the very special EPW sextic studied by Donten--Bury et alii. We also prove some other results concerning the Chow groups of this very special EPW sextic, and of certain related hyperk\"ahler fourfolds.
received 22.06.2016, accepted 28.08.2017 (27 pages)IRMA Université de Strasbourg 7, rue René Descartes 67084 Strasbourg cedex France IRMAR Université de Rennes 1 Campus de Beaulieu 35042 Rennes cedex France
Abstract: Let $p$ be a prime number, $V$ a complete discrete valuation ring of unequal caracteristics $(0,p)$, $G$ a smooth affine
algebraic group over $Spec \,V$. Using partial divided powers techniques of Berthelot, we construct arithmetic
distribution algebras, with level $m$, generalizing the classical construction of the distribution algebra.
We also construct the weak completion
of the classical distribution algebra over a finite extension $K$ of ${\bf Q}_p$ .
We then show that these distribution algebras can be identified with
invariant arithmetic differential operators over $G$, and prove a coherence result when the ramification index of $K$ is $
Dipartimento di Matematica e Applicazioni Università di Napoli Federico II Complesso Universitario Monte S. Angelo Via Cintia, Napoli Italy
Abstract: A class of groups {\mgoth X} is said to be countably recognizable if a group belongs to~{\mgoth X} whenever all its countable subgroups lie in {\mgoth X}. It is proved here that the class of groups whose subgroups are closed in the profinite topology is countably recognizable. Moreover, countably detectable properties of the finite residual of a group are studied.
received 17.01.2017, accepted 29.05.2017 (11 pages)Department of Mathematics Edificio Mario Laserna Cra 1 Este No 19A 40 Bogota Colombia Universidad de los Andes Colombia
Abstract: We study the ramified Cauchy problem for a linear PDE with a radial point using the theory of microdifferential operators.
received 23.09.2016, accepted 11.05.2017 (20 pages)Dipartimento di Matematica e Fisica III Università di Roma Largo San Leonardo Murialdo, 1 00146 Roma Italy Dipartimento di Matematica II Università di Roma “Tor Vergata” Via della Ricerca Scientifica 00133 Roma Italy
Abstract: We define a class of compact homogeneous $CR$ manifolds which are bases of Mostow fibrations having total spaces equal to their canonical complex realizations and Hermitian fibers. This is used to establish isomorphisms between their tangential Cauchy-Riemann cohomology groups and the corresponding Dolbeault cohomology groups of the embeddings.
received 17.12.2016, accepted 09.05.2017 (30 pages)RUDN University S. M. Nikol’skii Institute 6 Miklukho-Maklay St Moscow, 117198 Russia
Abstract: We introduce a class of Morrey-type spaces $M^\lambda_{p,q}$, which includes classical Morrey spaces and discuss their properties. We prove a Marcinkiewicz-type interpolation theorem. This theorem is then applied to obtaining the boundedness in the introduced Morrey-type spaces of the Riesz potential and singular integral operator.
received 05.10.2016, accepted 26.04.2017 (20 pages)Institut de Mathématiques de Jussieu - PRG Case 247 4 place Jussieu 75252 Paris Cedex 05 France
Abstract: We show in many cases the existence of adjoints to extension of scalars on categories of motivic nature, in the framework of field extensions. This is to be contrasted with the more classical situation where one deals with a finite type morphism of schemes. Among various applications, one is a construction of a ``Tate-\v Safarevi\v c motive" attached to an abelian variety over a function field. We also deduce a possible approach to \text{Bloch's} conjecture on surfaces, by reduction to curves.
received 18.11.2015, accepted 22.03.2017 (44 pages)Dipartimento di Matematica "F. Enriques" Università degli Studi di Milano Via C. Saldini, 50 I-20133 Milano Italy School of Mathematics University of Manchester Oxford Road Manchester M13 9PL UK
Abstract: Making use of Freyd's free abelian category on a preadditive category we show that if $T:D\rightarrow \mathcal{A}$ is a representation of a quiver $D$ in an abelian category $\mathcal{A}$ then there is an abelian category $\mathcal{A} (T)$, a faithful exact functor $F_T: \mathcal{A} (T) \to \mathcal{A}$ and an induced representation $\tilde T: D \to \mathcal{A} (T)$ such that $F_T\tilde T= T$ universally. We then can show that $\mathbb{T}$-motives as well as Nori's motives are given by a certain category of functors on definable categories.
received 03.10.2016, accepted 15.03.2017 (18 pages)Department of Mathematics Whitman College Walla Walla, WA 99362 USA
Abstract: \textit{Nunke's Problem} asks when the torsion product of two abelian $p$-groups is a direct sum of countable reduced groups. In previous work the author gave a complete answer to this question when the groups involved have countable length. In this paper a complete answer is given in the case of groups of uncountable length, at least in any set-theoretic universe in which $2^{\aleph_1}=\aleph_2$.
received 18.01.2017, accepted 03.03.2017 (18 pages)School of Science Nanjing University of Science and Technology Nanjing 210094 P. R. China
Abstract: In this paper we study the isoperimetric problem in a class of $x$-spherically symmetric sets in the Grushin space $\mathbb{R}^{h+1}$ with density $|x|^p$, $p>-h+1$. First we prove the existence of weighted isoperimetric sets. Then we deduce that, up to a vertical translation, a dilation and a negligible set, the weighted isoperimetric set is only of the form $\big\{(x,y)\in \mathbb{R}^{h+1}:|y|<\int_{\arcsin|x|}^{\frac{\pi}{2}}\sin^{\alpha+1}(t)dt,\hspace{2mm}|x|<1\big\}$.
received 31.01.2017, accepted 24.02.2017 (17 pages)Faculty of Mathematics Al. I. Cuza University Iasi Romania
Abstract: In this paper we introduce and study the concept of cyclic subgroup commutativity degree of a finite group $G$. This quantity measures the probability of two random cyclic subgroups of $G$ commuting. Explicit formulas are obtained for some particular classes of groups. A criterion for a finite group to be an Iwasawa group is also presented.
received 13.12.2016, accepted 21.02.2017 (15 pages)Instytut Matematyczny PAN Ul. Sniadeckich 8 00-656 Warsawa Poland
Abstract: We introduce a general formalism with minimal requirements under which we are able to prove the pro-modular Fontaine-Mazur conjecture. We verify it in the ordinary case using the recent construction of Breuil and Herzig.
received 04.07.2016, accepted 13.02.2017 (22 pages)School of Mathematics and Statistics Jiangsu Normal University Xuzhou, 221116 China lcw2000@126.com
Abstract: In this paper, we give some new characterizations of finite $p$-nilpotent groups by using the notion of $\mathcal{H}C$-subgroups and extend several recent results.
received 28.09.2016, accepted 17.01.2017 (8 pages)Department of Mathematics University of Science and Technology of China Hefei, 230026 P.R. China Department of Mathematics University of Science and Technology of China Hefei, 230026 P.R. China School of Mathematics and Statistics Jiangsu Normal UniversityXuzhou, 22 1116 P.R. China
Abstract: Let $\mathfrak{F}$ be a class of finite groups, $p$ a prime and $\pi$ a set of some primes. A finite group $G$ is called a $p$-quasi-$\mathfrak{F}$-group (respectively, by $\pi$-quasi-$\mathfrak{F}$-group) provided that for every $\mathfrak{F}$-eccentric $G$-chief factor $H/K$ of order divisible by $p$ (respectively, by at least one prime in $\pi$), the automorphisms of $H/K$ induced by all elements of $G$ are inner. In this paper, we obtain the characterizations of $p$-quasi-$\mathfrak{F}$-groups and $\pi$-quasi-$\mathfrak{F}$-groups, which give a positive answer to an open problem in the book [3].
received 29.07.2016, accepted 04.11.2016 (8 pages)Department of Mathematics Shanghai University Shanghai 200444 P. R. China
Abstract: A subgroup $H$ of a finite group $G$ is said to be $W$-$S$-permutable in $G$ if there is a subgroup $K$ of $G$ such that $G=HK$ and $H\cap K$ is a nearly $S$-permutable subgroup of $G$. In this article, we analyse the structure of a finite group $G$ by using the properties of $W$-$S$-permutable subgroups and obtain some new characterizations of finite $p$-nilpotent groups and finite supersolvable groups. Some known results are generalized.
received 20.04.2016, accepted 06.10.2016 (12 pages)Guo Zhang Department of Mathematics University of Science and Technology of China Hefei 230026 P. R. China Skiba Sinitsa Department of Mathematics Francisk Skorina Gomel State University Gomel 246019 Belarus
Abstract: Let $G$ be a finite group. Let $\sigma =\{\sigma_{i} | i\in I\}$ be a partition of the set of all primes $\Bbb{P}$ and $n$ an integer. We write $\sigma (n) =\{\sigma_{i} |\sigma_{i}\cap \pi (n)\ne \emptyset \}$, $\sigma (G) =\sigma (|G|)$. A set $ {\cal H}$ of subgroups of $G$ is said to be a complete Hall $\sigma $-set of $G$ if every member of ${\cal H}\setminus \{1\}$ is a Hall $\sigma _{i}$-subgroup of $G$ for some $\sigma _{i}$ and ${\cal H}$ contains exact one Hall $\sigma _{i}$-subgroup of $G$ for every $\sigma _{i}\in \sigma (G)$. A subgroup $A$ of $G$ is called: (i) a $\sigma$-Hall subgroup of $G$ if $\sigma (A) \cap \sigma (|G:A|)=\emptyset$; (ii) ${\sigma}$-permutable in $G$ if $G$ possesses a complete Hall $\sigma$-set ${\cal H}$ such that $AH^{x}=H^{x}A$ for all $H\in {\cal H}$ and all $x\in G$. We say that a subgroup $A$ of $G$ is $H_{\sigma}$-permutably embedded in $G$ if $A$ is a ${\sigma}$-Hall subgroup of some ${\sigma}$-permutable subgroup of $G$. We study finite groups $G$ having an $H_{\sigma}$-permutably embedded subgroup of order $|A|$ for each subgroup $A$ of $G$. Some known results are generalized.
received 07.06.2016, accepted 18.08.2016 (13 pages)