Related papers: Half-isomorphisms whose inverses are also half-iso…

The paper deals with quasigroups having a trivial group of automorphisms and a trivial group of autotopisms. Examples of such quasigroups and methods of their verification are given.

Let $G$ be a finite $p$-group and let Aut$(G)$ denote the full automorphism group of $G$. In the recent past, there has been interest in finding necessary and sufficient conditions on $G$ such that certain subgroups of Aut$(G)$ are equal.…

In this paper we prove that every automorphism of the semigroup of invertible matrices with nonnegative elements over a linearly oredered associative ring on some specially defined subgroup concides with the composition of an inner…

In this paper, we characterize completely the structure of Clifford semigroups of matrices over an arbitrary field. It is shown that a semigroups of matrices of finite order is a Clifford semigroup if and only if it is isomorphic to a…

The Subgroup Isomorphism Problem for Integral Group Rings asks for which finite groups U it is true that if U is isomorphic to a subgroup of V(ZG), the group of normalized units of the integral group ring of the finite group G, it must be…

Among the simplest invariants of the sporadic finite simple groups are their outer automorphism groups. For 12 of the 26 possible isomorphism types of a sporadic simple group G, the outer automorphism group Out(G) has order 2, and in the…

In this paper is proved that the group of automorphisms of semigroup End(P[X]), if P is algebraically closed field, is generated by semi-inner automorphisms.

For a classical group $G$ over a field $F$ together with a finite-order automorphism $\theta$ that acts compatibly on $F$, we describe the fixed point subgroup of $\theta$ on $G$ and the eigenspaces of $\theta$ on the Lie algebra…

An answer to the question investigated in this paper brings a new characterization of internal groupoids such that: (a) it holds even when finite limits are not assumed to exist; (b) it is a full subcategory of the category of…

Let $S,T$ be two numerical semigroups. We study when $S$ is one half of $T$, with $T$ almost symmetric. If we assume that the type of $T$, $t(T)$, is odd, then for any $S$ there exist infinitely many such $T$ and we prove that $1 \leq t(T)…

Orbits of automorphism groups of partially ordered sets are not necessarily congruence classes, i.e. images of an order homomorphism. Based on so-called orbit categories a framework of factorisations and unfoldings is developed that…

For an Abelian group $G$, any homomorphism $\mu\colon G\otimes G\rightarrow G$ is called a \textsf{multiplication} on $G$. The set $\text{Mult}\,G$ of all multiplications on an Abelian group $G$ is an Abelian group with respect to addition.…

We prove that the order of an ordered group is an interval order if and only if it is a semiorder. Next, we prove that every semiorder is isomorphic to a collection $\mathcal J$ of intervals of some totally ordered abelian group, these…

We determine the automorphism group for some well known constructions of finite semifields. In particular, we compute the automorphism group of Sandler's semifields and in certain cases the automorphism groups of the Hughes-Kleinfeld and…

Let $\mathcal C$ be a class of topological semigroups. A semigroup $X$ is called $absolutely$ $\mathcal C$-$closed$ if for any homomorphism $h:X\to Y$ to a topological semigroup $Y\in\mathcal C$, the image $h[X]$ is closed in $Y$. Let…

Structures of commuting semigroups of isometries under certain additional assumptions like double commutativity or dual double commutativity are found.

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…

In \cite{Oh22}, the second author defined a complex of groups decomposition of the fundamental group of a finitely generated 2-dimensional special group, called an \emph{intersection complex}, which is a quasi-isometry invariant. In this…

Let $V$ and $W$ be finite dimensional real vector spaces and let $G\subset\GL(V)$ and $H\subset\GL(W)$ be finite subgroups. Assume for simplicity that the actions contain no reflections. Let $Y$ and $Z$ denote the real algebraic varieties…

A finite group $G$ admits an {\em oriented regular representation} if there exists a Cayley digraph of $G$ such that it has no digons and its automorphism group is isomorphic to $G$. Let $m$ be a positive integer. In this paper, we extend…