Related papers: Finite permutation groups containing a regular dih…

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…

In this short note we present a simple combinatorial trick which can be effectively applied to show the non--existence of sharply transitive sets of permutations in certain finite permutation groups.

We introduce a discrete deformation of Rieffel type for finite (quantum) groups. Using this, we give a non-trivial example of a finite quantum group of order 18. We also give a deformation of finite groups of Lie type by using their maximal…

We show that a finite permutation group containing a regular abelian self-normalizing subgroup is soluble.

We study finite transitive permutation groups $G\leqslant\operatorname{Sym}(\Omega)$ such that all orbits of the conjugation action on $G$ of the normaliser of $G$ in $\operatorname{Sym}(\Omega)$ have size bounded by some constant. Our…

We give an account on what is known on the subject of permutation matchings, which are bijections of a finite regular semigroup that map each element to one of its inverses. This includes partial solutions to some open questions, including…

We present new classes of permutation polynomials over finite fields.

For each finite classical group $G$, we classify the subgroups of $G$ which act transitively on a $G$-invariant set of subspaces of the natural module, where the subspaces are either totally isotropic or nondegenerate. Our proof uses the…

We describe all closed permutation groups which act on the set of vectors of a countable vector space $V$ over a prime field of odd order and which contain all automorphisms of $V$. In particular, we prove that their number is finite. These…

In this paper, we discuss some well-known results and some open problems of the theory of $\sigma$-properties of a group related to the study of generalized $T$-groups.

We give a characterization of limits of dihedral groups in the space of finitely generated marked groups. We also describe the topological closure of dihedral groups in the space of marked groups on a fixed number of generators.

In this paper, we classify the finite simple groups with an abelian Sylow subgroup.

In this paper we introduce and study the relative cyclic subgroup commutativity degrees of a finite group. We show that there is a finite group with $n$ such degrees for all $n \in \mathbb{N}^*\setminus \lbrace 2\rbrace$ and we indicate…

A quasi-semiregular element in a permutation group is an element that has a unique fixed point and acts semiregularly on the remaining points. Such elements were first studied in the context of automorphisms of graphs and occur naturally in…

We classify all finite groups with five relative commutativity degrees. Also, we give a partial answer to our previous conjecture on a lower bound of the number of relative commutativity degrees of finite groups.

A classification of finite groups in which every 3-maximal subgroup is K-U-subnormal is given.

We give an example of a finitely presented simple group containing a finitely generated subgroup which is not finitely presented.

We determine the finite groups whose real irreducible representations have different degrees.

We present an explicit formula for subregular characters (i.e, irreducible finite-dimensional complex characters of submaximal degree) of the unitriangular group over a finite field of sufficiently large characteristic.

The commutativity degree of a finite group is the probability that two randomly chosen group elements commute. The main object of this paper is to obtain a characterization for all finite groups of odd order with commutativity degree…