International Journal of Group Theory
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Enumerating word maps in finite groups
(University of Isfahan, 20240901)We consider word maps over finite groups. An $n$variable word $w$ is an element of the free group on $n$symbols. For any group $G$, a word $w$ induces a map from $G^n\mapsto G$ where $(g_1,\ldots,g_n)\mapsto w(g_1,\ldots,g_n)$. ...

Covering perfect hash families and covering arrays of higher index
(University of Isfahan, 20240901)By exploiting symmetries of finite fields, covering perfect hash families provide a succinct representation for covering arrays of index one. For certain parameters, this connection has led to both the best current asymptotic ...

Nonseparable matrix builders for signal processing, quantum information and mimo applications
(University of Isfahan, 20240901)Matrices are built and designed by applying procedures from lower order matrices. Matrix tensor products, direct sums or multiplication of matrices are such procedures and a matrix built from these is said to be a separable ...

Orders of simple groups and the BatemanHorn Conjecture
(University of Isfahan, 20240901)We use the BatemanHorn Conjecture from number theory to give strong evidence of a positive answer to Peter Neumann's question, whether there are infinitely many simple groups of order a product of six primes. (Those with ...

On the proportion of elements of prime order in finite symmetric groups
(University of Isfahan, 20240901)We give a short proof for an explicit upper bound on the proportion of permutations of a given prime order $p$, acting on a set of given size $n$, which is sharp for certain $n$ and $p$. Namely, we prove that if $n\equiv ...

Computing Galois groups
(University of Isfahan, 20240901)The determination of a Galois group is an important question in computational algebraic number theory. One approach is based on the inspection of resolvents. This article reports on this method and on the performance of ...

New constructions of Deza digraphs
(University of Isfahan, 20240901)Deza digraphs were introduced in 2003 by Zhang and Wang as directed graph version of Deza graphs, that also generalize the notion of directed strongly regular graphs. In this paper, we give several new constructions of ...

On the theory and generalization of $\Sigma$groups
(University of Isfahan, 20240601)In this work we present a systematic study of $n$layered modules which are closely related to $\Sigma$modules. For each integer $n \geq 1$ we prove some results for $n$layered modules concerning when $\Sigma$modules ...

Groups having $11$ cyclic subgroups
(University of Isfahan, 20240601)Let $c(G)$ denotes the number of cyclic subgroups of a finite group $G$. A group $G$ is said to be {\em $n$cyclic}, if $c(G)=n$. In this paper, we classify all $11$cyclic groups.

Average order in regular wreath products
(University of Isfahan, 20240601)We obtain an exact formula for the average order of elements of regular wreath product of two finite groups. Then focussing our attention on $p$groups for primes $p$, we give an estimate for the verage order of a wreath ...

The probability of zero multiplication in finite group algebras
(University of Isfahan, 20240601)Let $\mathbb{F}_qG$ be a finite group algebra. We denote by $P(\mathbb{F}_qG)$ the probability that the product of two elements of $\mathbb{F}_qG$ be zero. In this paper, we obtain several results on this probability ...

Structure of finite groups with trait of nonnormal subgroups II
(University of Isfahan, 20240601)A finite nonDedekind group $G$ is called an 𝒩𝒜𝒞group if all nonnormal abelian subgroups are cyclic. In this paper, all finite 𝒩𝒜𝒞groups will be characterized. Also, it will be shown that the center of nonnilpotent ...

Cubic semisymmetric graphs of order $44p$ or $44p^{2}$
(University of Isfahan, 20240601)A simple graph is called semisymmetric if it is regular and edgetransitive but not vertextransitive. Let $p$ be an arbitrary prime. Folkman [J. Folkman, Regular linesymmetric graphs, J. Combinatorial Theory, \textbf{3} ...

GowTamburini type generation of the special linear group for some special rings.
(University of Isfahan, 20240601)Let $R$ be a commutative ring with unity and let $n\geq 3$ be an integer. Let $SL_n(R)$ and $E_n(R)$ denote respectively the special linear group and elementary subgroup of the general linear group $GL_n(R).$ A result of ...

Posetblowdowns of generalized quaternion groups
(University of Isfahan, 20240601)Posetblowdown of subgroup posets of groups is an analog of blowdown in algebraic geometry. It is a poset map obtained by contracting normal subgroups. For finite groups, this is considered as a map between the Hasse ...

An example of a quasicommutative inverse semigroup
(University of Isfahan, 20240301)Constructing concrete examples of certain semigroups could help in implementing algorithms optimized for the users. We give concrete examples of certain finitely presented semigroups, namely $S_{p,n}$. Both computational ...

Noninner automorphisms of order $p$ in finite $p$groups of coclass $4$ and $5$
(University of Isfahan, 20240301)A longstanding conjecture asserts that every finite nonabelian $p$group has a noninner automorphism of order $p$. This paper proves the conjecture for finite $p$groups of coclass $4$ and $5$ ($p\ge 5$). We also prove ...

Orbits classifying extensions of prime power order groups
(University of Isfahan, 20240301)The strong isomorphism classes of extensions of finite groups are parametrized by orbits of a prescribed action on the second cohomology group. We study these orbits in the case of extensions of a finite abelian $p$group ...

The influence of $\mathscr{H}$subgroups on $p$nilpotency and $p$supersolvability of finite groups
(University of Isfahan, 20240301)Let $G$ be a finite group. A subgroup $H$ of $G$ is an $\mathscr{H}$subgroup in $G$ if $N_G(H)\cap H^g \leq H$ for any $g \in G$. In this article, by using the concept of $\mathscr{H}$subgroups, we study the influence ...

On Neumann’s BFCtheorem and finitebynilpotent profinite groups
(University of Isfahan, 20240301)Let $\gamma_{n}=[x_{1},\ldots,x_{n}]$ be the $n$th lower central word and $X_{n}(G)$ the set of $\gamma_{n}$values in a group $G$. Suppose that $G$ is a profinite group where, for each $g\in G$, there exists a positive ...