Related papers: On pseudobounded and premeager paratopological gro…

A closed subgroup $H$ of a locally compact group $G$ is confined if the closure of the conjugacy class of $H$ in the Chabauty space of $G$ does not contain the trivial subgroup. We establish a dynamical criterion on the action of a totally…

Let $G$ be a finite permutation group acting on $\Omega$. A base for $G$ is a subset $B \subseteq \Omega$ such that the pointwise stabilizer $G_{(B)}$ is the identity. The base size of $G$, denoted by $b(G)$, is the cardinality of the…

We continue the analysis of definably compact groups definable in a real closed field $\mathcal{R}$. In [3], we proved that for every definably compact definably connected semialgebraic group $G$ over $\mathcal{R}$ there are a connected…

Throughout this paper, all groups are finite. Let $\sigma =\{\sigma_{i} | i\in I \}$ be some partition of the set of all primes $\Bbb{P}$. If $n$ is an integer, the symbol $\sigma (n)$ denotes the set $\{\sigma_{i} |\sigma_{i}\cap \pi…

We provide characterizations of Lie groups as compact-like groups in which all closed zero-dimensional metric (compact) subgroups are discrete. The "compact-like" properties we consider include (local) compactness, (local)…

We consider an arbitrary topological group $G$ definable in a structure $\mathcal M$, such that some basis for the topology of $G$ consists of sets definable in $\mathcal M$. To each such group $G$ we associate a compact $G$-space of…

Let $G$ be an infinite simple group of finite Morley rank and $\alpha$ a supertight automorphism of $G$ so that the fixed point subgroup $P_n:=C_G(\alpha^n)$ is pseudofinite for all $n\in \mathbb{N}\setminus\{0\}$. It is know (using CFSG)…

The class of finitely presented algebras over a field $K$ with a set of generators $a_{1},\ldots , a_{n}$ and defined by homogeneous relations of the form $a_{1}a_{2}\cdots a_{n} =a_{\sigma (1)} a_{\sigma (2)} \cdots a_{\sigma (n)}$, where…

Let $G$ be a locally compact topological group, $G_0$ the connected component of its identity element, and comp(G) the union of all compact subgroups. A topological group will be called inductively monothetic if any subgroup generated (as a…

Let $p$ be a prime and $F$ be a finite field of characteristic $p$. Suppose that $FG$ is the group algebra of the finite $p$-group $G$ over the field $F$. Let $V(FG)$ denote the group of normalized units in $FG$ and let $V_*(FG)$ denote the…

We consider presymplectic manifolds equipped with Hamiltonian G-actions, G being a connected compact Lie group. A presymplectic manifold is foliated by the integral submanifolds of the kernel of the presymplectic form. For a presymplectic…

We give new characterizations of sofic groups: -- A group $G$ is sofic if and only if it is a subgroup of a quotient of a direct product of alternating or symmetric groups. -- A group $G$ is sofic if and only if any system of equations…

Let $G$ be a transitive permutation group acting on a finite set $\Omega$ with $|\Omega|\geqslant 2$. An element of $G$ is said to be a derangement if it has no fixed points on $\Omega$, and by a theorem of Jordan from 1872, $G$ always…

Let $M$ be a compact, connected manifold of positive dimension and let $\mathcal G\leq\textrm{Homeo}(M)$ be \emph{locally approximating} in the sense that for all open $U\subseteq M$ compactly contained in a single Euclidean chart of $M$,…

A Hausdorff paratopological group G is H-closed if G is closed in each Hausdorff paratopological group containing G. We obtain criteria of H-closedness for some classes of abelian paratopological groups. In particular, for topological…

Suppose that $G$ is a finite group and $H$ is a subgroup of $G$. We say that $H$ is s-semipermutable in $G$ if $HG_p = G_pH$ for any Sylow $p$-subgroup $G_p$ of $G$ with $(p, |H|) = 1$. We investigate the influence of s-semipermutable…

The so--called subgroup commutativity degree $sd(G)$ of a finite group $G$ is the number of permuting subgroups $(H,K) \in \mathrm{L}(G) \times \mathrm{L}(G)$, where $\mathrm{L}(G)$ is the subgroup lattice of $G$, divided by…

We show that every definable group G in an o-minimal structure is definably finitely generated. That is, G contains a finite subset that is not included in any proper definable subgroup. This provides another proof, and a generalization to…

A 2-covering for a finite group $G$ is a set of proper subgroups of $G$ such that every pair of elements of $G$ is contained in at least one subgroup in the set. The minimal number of subgroups needed to 2-cover a group $G$ is called the…

A subgroup $H$ of a group $G$ is called $\mathbb P$-subnormal in $G$ whenever either $H=G$ or there is a chain of subgroups $H=H_0\subset H_1\subset ... \subset H_n=G$ such that $|H_i:H_{i-1}|$ is a prime for all $i$. In this paper, we…