Related papers: The automorphism group of the sandwich inverse sym…

The structure of a certain subgroup $S$ of the automorphism group of a partially commutative group (RAAG) $G$ is described in detail: namely the subgroup generated by inversions and elementary transvections. We define admissible subsets of…

By an automorphism of a topological group G we mean an isomorphism of G onto itself which is also a homeomorphism. In this article, we study the automorphism group Aut(G) of a dense subgroup G of R^n, n>=1. We show that Aut(G) can be…

Starting from the symmetric group $S_n$, we construct two fiat $2$-categories. One of them can be viewed as the fiat "extension" of the natural $2$-category associated with the symmetric inverse semigroup (considered as an ordered semigroup…

We describe the structure of the algebraic group of automorphisms of all simple finite dimensional Lie superalgebras. Using this and \'etale cohomology considerations, we list all different isomorphism classes of the corresponding twisted…

In answer to a question of P. Hall, we supply another construction of a group which is isomorphic to each of its non-trivial normal subgroups.

In this paper, the complete algebraic structure of finite semisimple group algebra of a normally monomial group is described. The main result is illustrated by computing the explicit Wedderburn decomposition of finite semisimple group…

We will review the main results concerning the automorphism groups of saturated structures which were obtained during the two last decades. The main themes are: the small index property in the countable and uncountable cases; the…

The description of the automorphism group of group $<a, b; [a^m,b^n]=1>$ ($m,n>1$) in terms of generators and defining relations is given. This result is applied to prove that any normal automorphism of every such group is inner.

In this paper we study the automorphism group of a possible symmetric $(81,16,3)$ design.

While every group is isomorphic to a transitive group of permutations, the analogous property fails for inverse semigroups: not all inverse semigroups are isomorphic to transitive inverse semigroups of one-to-one partial transformations of…

An inverse semigroup $S$ is a semigroup in which every element has a unique inverse in the sense of semigroup theory, that is, if $a \in S$ then there exists a unique $b\in S$ such that $a = aba$ and $b = bab$. We say that an inverse…

Let $S_n$ and $A_n$ denote the symmetric group and alternating group of degree $n$ with $n\geq 3$, respectively. Let $S$ be the set of all $3$-cycles in $S_n$. The \emph{complete alternating group graph}, denoted by $CAG_n$, is defined as…

We construct the \emph{inverse partition semigroup} $\mathcal{IP}_X$, isomorphic to the \emph{dual symmetric inverse monoid} $\mathcal{I}^{\ast}_X$, introduced in [6]. We give a convenient geometric illustration for elements of…

We show that the holomorph of a cyclic group of order $n$ is isomorphic to its own automophism group when $n$ is twice of a power of an odd prime.

We introduce two generalisations of the full symmetric inverse semigroup ${\mathcal{I}}_X$ and its dual semigroup ${\mathcal{I}^{\ast}}_X$ -- inverse semigroups ${\mathcal{PI}^{\ast}}_X$ and ${\overline{\mathcal{PI}^{\ast}}}_X$. Both of…

We construct quasi-isometric embeddings from right-angled Artin groups into the outer automorphism group of a free group. These homomorphisms are in analogy with those constructed in \cite{CLM}, where the target group is the mapping class…

In this paper we construct two groupoids from morphisms of groupoids, with one from a categorical viewpoint and the other from a geometric viewpoint. We show that for each pair of groupoids, the two kinds of groupoids of morphisms are…

In this paper the number of isomorphism classes of the right transversals of the symmetric group $\Sigma_{n-1}$ in the symmetric group $\Sigma_n$ is calculated. This result together with the techniques employed along the paper may be used…

We consider a version of the notion of F-inverse semigroup (studied in the algebraic theory of inverse semigroups). We point out that an action of such an inverse semigroup on a locally compact space has associated a natural groupoid…

The modified bubble-sort graph of dimension $n$ is the Cayley graph of $S_n$ generated by $n$ cyclically adjacent transpositions. In the present paper, it is shown that the automorphism group of the modified bubble sort graph of dimension…