Related papers: Algorithms for twisted conjugacy classes of polycy…

We address the question: for which collections of finite simple groups does there exist an algorithm that determines the images of an arbitrary finitely presented group that lie in the collection? We prove both positive and negative…

We consider the conjugation-action of an arbitrary upper-block parabolic subgroup of the general linear group on the variety of nilpotent matrices in its Lie algebra. Lie-theoretically, it is natural to wonder about the number of orbits of…

Leech's (co)homology groups of finite cyclic monoids are computed.

In this paper we prove the trace formulas for the Reidemeister numbers of group endomorphisms in the following cases:the group is finitely generated and an endomorphism is eventually commutative; the group is finite ; the group is a direct…

In this note we give presentations of all finite subgroups of the mapping class group of a closed surface of genus 2 by the Humphries generators up to conjugacy.

We classify all finite groups G such that the product of any two non-inverse conjugacy classes of G is always a conjugacy class of G. We also classify all finite groups G for which the product of any two G-conjugacy classes which are not…

Among restricted wreath products $G\wr \mathbb Z^k $, where $G$ is a finite Abelian group, we find three large classes of groups admitting an automorphism $\varphi$ with finite Reidemeister number $R(\varphi)$ (number of $\varphi$-twisted…

We describe the twisted doubling integrals of Cai-Friedberg-Ginzburg-Kaplan in a conceptual way. This also extends the construction to the quaternionic unitary groups. We carry out the unfolding argument uniformly in this article. To do so,…

The finite groups having an indecomposable polynomial invariant whose degree is at least half of the order of the group are classified. Apart from four sporadic exceptions these are exactly the groups having a cyclic subgroup of index at…

The problem of finding the number of ordered commuting tuples of elements in a finite group is equivalent to finding the size of the solution set of the system of equations determined by the commutator relations that impose commutativity…

Let $k$ be a regular ring, and let $A,B$ be essentially finite type $k$-algebras. For any functor $F:{D}(A)\times\dots\times{D}(A)\to{D}(B)$ between their derived categories, we define its twist…

We associate each endomorphism of a finite cyclic group with a digraph and study many properties of this digraph, including its adjacent matrix and automorphism group.

In this paper, we set $\eta (G)$ to be the number of conjugacy classes of maximal cyclic subgroups of a finite group $G$. We compute $\eta (G)$ for all metacyclic $p$-groups. We show that if $G$ is a metacyclic $p$-group of order $p^n$ that…

We consider two algorithms which can be used for proving positivity of sequences that are defined by a linear recurrence equation with polynomial coefficients (P-finite sequences). Both algorithms have in common that while they do succeed…

We continue our investigation of a variation of the group ring isomorphism problem for twisted group algebras. Contrary to previous work, we include cohomology classes which do not contain any cocycle of finite order. This allows us to…

If a soluble group $G$ contains two finitely generated abelian subgroups $A,B$ such that the number of double cosets $AgB$ is finite, then $G$ is shown to be virtually polycyclic.

In this paper we introduce and study the concept of cyclic factorization number of a finite group G. By using the Mobius inversion formula and other methods involving the cyclic subgroup structure, this is explicitly computed for some…

We prove that if two finite metacyclic groups have isomorphic rational group algebras, then they are isomorphic. This contributes to understand where is the line separating positive and negative solutions to the Isomorphism Problem for…

An algorithm for the explicit computation of a complete set of primitive central idempotents, Wedderburn decomposition and the automorphism group of the semisimple group algebra of a finite metabelian group is developed. The algorithm is…

We study the problem of determining the isomorphism classes of the virtually cyclic subgroups of the n-string braid groups B_n(S^2) of the 2-sphere S^2. If n is odd, or if n is even and sufficiently large, we obtain the complete…