Related papers: Redundant relators in cyclic presentations of grou…

Let $G$ be a finite group and construct a graph $\Delta(G)$ by taking $G\setminus\{1\}$ as the vertex set of $\Delta(G)$ and by drawing an edge between two vertices $x$ and $y$ if $\langle x,y\rangle$ is cyclic. Let $K(G)$ be the set…

This article initiates a geometric study of the automorphism groups of general graph products of groups, and investigates the algebraic and geometric structure of automorphism groups of cyclic product of groups. For a cyclic product of at…

We describe the structure of the irreducible representations of crossed products of unital C*-algebras by actions of finite groups in terms of irreducible representations of the C*-algebras on which the groups act. We then apply this…

For a cyclic group $a$, define the atom of $a$ as the set of all elements generating $a$. Given any two elements $a,b$ of a finite cyclic group $G$, we study the sumset of the atom of $a$ and the atom of $b$. It is known that such a sumset…

We give a complete list of orbit codes that are generated by an irreducible cyclic group, i.e. an irreducible group having one generator. We derive some of the basic properties of these codes such as the cardinality and the minimum…

Let $N_{g,n}$ denote the nonorientable surface of genus $g$ with $n$ boundary components and $M(N_{g,n})$ its mapping class group. We obtain an explicit finite presentation of $M(N_{g,n})$ for $n=0,1$ and all $g$ such that $g+n>3$.

We find a family of groups generated by a pair of parabolic elements in which every relator must admit a long subword of a specific form. In particular, this collection contains groups in which the number of syllables of any relator is…

First, I construct an isomorphism between the categories of (topological) groups of nilpotency class 2 with 2-divisible center and (topological) Lie rings of nilpotency class 2 with 2-divisible center. That isomorphism allows us to…

We call $n$ a cyclic number if every group of order $n$ is cyclic. It is implicit in work of Dickson, and explicit in work of Szele, that $n$ is cyclic precisely when $\gcd(n,\phi(n))=1$. With $C(x)$ denoting the count of cyclic $n\le x$,…

A fundamental theorem in the study of Dunwoody manifolds is a classification of finite graphs on $2n$ vertices that satisfy seven conditions (concerning planarity, regularity, and a cyclic automorphism of order $n$). Its significance is…

All crossed products of two cyclic groups are explicitly described using generators and relations. A necessary and sufficient condition for an extension of a group by a group to be a cyclic group is given.

A parametrization of irreducible representations associated with a regular adjoint orbit of a classical group over finite quotient rings of the ring of integer of a non-dyadic non-archimedean local field is presented. The parametrization is…

This is the third, and last, of a series of papers dealing with oriented regular representations. Here we complete the classification of finite groups that admit an oriented regular representation (or ORR for short), and give a complete…

We determine the eigenvalues with multiplicity of each element of an alternating group in any irreducible representation. This is equivalent to determining the decomposition of cyclic representations of alternating groups into irreducibles.…

In the acyclic case, we establish a one-to-one correspondence between the tilting objects of the cluster category and the clusters of the associated cluster algebra. This correspondence enables us to solve conjectures on cluster algebras.…

We give a parametrization of cyclic pointed categories associated to the cyclic group of order $n$ in terms of $n$-th roots of unity. We also provide a diagramatic description of these categories by generators and relations, and use it to…

In this paper we determine the irreducible projective representations of sporadic simple groups over an arbitrary algebraically closed field F, whose image contains an almost cyclic matrix of prime-power order. A matrix M is called cyclic…

The notion of 'presentation', as used in combinatorial group theory, is applied to coded character sets(CCSs) - sets which facilitate the interchange of messages in a digital computer network(DCN) . By grouping each element of the set into…

By a rectangular distributive lattice we mean the direct product of two non-singleton finite chains. We prove that the retracts (ordered by set inclusion and together with the empty set) of a rectangular distributive lattice $G$ form a…

Complex reflection groups of rank two are precisely the finite groups in the family of groups that we call J-reflection groups. These groups are particular cases of J-groups as defined by Achar & Aubert in 2008. The family of J-reflection…