Related papers: Conjugacy in inverse semigroups

We consider the group G of R-automorphisms of the polynomial ring R[x] especially in the case where R is the ring of integers modulo n. We describe conjugacy classes in G, and in the case where n = 4, we describe more explicitly the…

Graph inverse semigroups generalize the polycyclic inverse monoids and play an important role in the theory of C*-algebras. This paper has two main goals: first, to provide an abstract characterization of graph inverse semigroups; and…

We study generalized inverses on semigroups by means of Green's relations. We first define the notion of inverse along an element and study its properties. Then we show that the classical generalized inverses (group inverse, Drazin inverse…

A conjugacy class $C$ of a finite group $G$ is a sign conjugacy class if every irreducible character of $G$ takes value 0, 1 or -1 on $C$. In this paper we classify the sign conjugacy classes of alternating groups.

A finite group $G$ is called uniformly semi-rational if there exists an integer $r$ such that the generators of every cyclic sugroup $\langle x \rangle$ of $G$ lie in at most two conjugacy classes, namely $x^G$ or $(x^r)^G$. In this paper,…

A completely inverse $AG^{**}$-groupoid is a groupoid satisfying the identities $(xy)z=(zy)x$, $x(yz)=y(xz)$ and $xx^{-1}=x^{-1}x$, where $x^{-1}$ is a unique inverse of $x$, that is, $x=(xx^{-1})x$ and $x^{-1}=(x^{-1}x)x^{-1}$. First we…

Let G be a word-hyperbolic group with given finite generating set, for which various standard structures and constants have been pre-computed. A (non-practical) algorithm is described that, given as input two lists A and B, each composed of…

Given a group G, the conjugacy problem in G is the problem of giving an effective procedure for determining whether or not two given elements f, g of G are conjugate, i.e. whether there exists h belonging to G with fh = hg. This paper is…

A special type of conjugacy classes in symmetric groups is studied and used to answer a question about odd-degree irreducible characters

A semigroup amalgam (S; T1, T2) is known to be non-embeddable if T1 and T2 are both groups (completely regular semigroups, Clifford semigroups) but S is not such. We prove some non-embeddability conditions for semigroup amalgams (S; T1, T2)…

Let G be a connected reductive group. We define a map from the set of unipotent classes in G to the set of conjugacy classes in the Weyl group (assuming that the characteristic is not bad). This map is a one sided inverse of a map in the…

Let $\mathsf G$ be a connected reductive linear algebraic group defined over $\mathbb R$, and let $C: \mathsf G\rightarrow \mathsf G$ be a fundamental Chevalley involution. We show that for every $g\in \mathsf G(\mathbb R)$, $C(g)$ is…

In this paper, we study the structure of finite groups with a large number of conjugacy classes of $p$-elements for some prime $p$. As consequences, we obtain some new criteria for the existence of normal $p$-complements in finite groups.

We introduce and study conjugate reversibility (or $c$-reversibility) in the complex special linear group $\SL(n,\C)$ where an element is conjugate to the inverse of its complex conjugate. We prove that in $\SL(n, \C)$, every $c$-reversible…

We construct new examples of non-nil algebras with any number of generators, which are direct sums of two locally nilpotent subalgebras. As all previously known examples, our examples are contracted semigroup algebras and the underlying…

The conjugacy problem for a finitely generated group $G$ is the two-variable problem of deciding for an arbitrary pair $(u,v)$ of elements of $G$, whether or not $u$ is conjugate to $v$ in $G$. We construct examples of finitely generated,…

In this work we present algebraic conditions on an inverse semigroup S (with zero) which imply that its associated tight groupoid G_{tight)(S) is: Hausdorff, essentially principal, minimal and contracting, respectively. In some cases these…

Many results have been established that show how arithmetic conditions on conjugacy class sizes affect group structure. A conjugacy class in $G$ is called vanishing if there exists some irreducible character of $G$ which evaluates to zero…

Let G' be a connected reductive group over the complex numbers. We show that the set of conjugacy classes of G' is in natural bijection with the set of two-sided cells associated to a certain algebra.

A closed subgroup of a semisimple algebraic group is called irreducible if it lies in no proper parabolic subgroup. In this paper we classify all irreducible subgroups of exceptional algebraic groups $G$ which are connected, closed and…