Related papers: Sharply doubly transitive groups with saturation c…

A transitive permutation group is semiprimitive if each of its normal subgroups is transitive or semiregular. Interest in this class of groups is motivated by two sources: problems arising in universal algebra related to collapsing monoids…

The finite sharply $2$-transitive groups were classified by Zassenhaus in the 1930's. They essentially all look like the group of affine linear transformations $x\mapsto ax+b$ for some field (or at least near-field) $K$. However, the…

We prove that, in both real and complex cases, there exists a pair of matrices that generates a dense subsemigroup of the set of $n\times n$ matrices.

The article deals with profinite groups in which the centralizers are abelian (CA-groups), that is, with profinite commutativity-transitive groups. It is shown that such groups are virtually pronilpotent. More precisely, let G be a…

By definition, admissible matrix groups are those that give rise to a wavelet-type inversion formula. This paper investigates necessary and sufficient admissibility conditions for abelian matrix groups. We start out by deriving a block…

A permutation group $G\le\operatorname{Sym}(\Omega)$ is said to be $2$-closed if no group $H$ such that $G<H\le\operatorname{Sym}(\Omega)$ has the same orbits on $\Omega\times\Omega$ as $G$. A simple and efficient inductive criterion for…

The sets of primitive, quasiprimitive, and innately transitive permutation groups may each be regarded as the building blocks of finite transitive permutation groups, and are analogues of composition factors for abstract finite groups. This…

For some countable discrete torsion Abelian groups we give examples of their finite measure-preserving actions which have simple spectrum and no approximate transitivity property.

A transitive permutation group is said to be semiprimitive if each of its normal subgroups is either semiregular or transitive.The class of semiprimitive groups properly contains primitive groups, quasiprimitive groups and innately…

In this paper we prove that if there is a regular Paley type partial difference set in an Abelian group $G$ of order $v$, where $v=p_1^{2k_1}p_2^{2k_2}\cdots p_n^{2k_n}$, $n\ge 2$, $p_1$, $p_2$, $\cdots$, $p_n$ are distinct odd prime…

Various descending chains of subgroups of a finite permutation group can be used to define a sequence of `basic' permutation groups that are analogues of composition factors for abstract finite groups. Primitive groups have been the…

A permutation group is said to be quasiregular if every its transitive constituent is regular, and a quasiregular coherent configuration can be thought as a combinatorial analog of such a group: the transitive constituents are replaced by…

This paper gives sufficient conditions for a class of bang-bang extremals with multiple switches to be locally optimal in the strong topology. The conditions are the natural generalizations of the ones considered in previous papers for more…

A semiregular permutation group on a set $\Ome$ is called {\em bi-regular} if it has two orbits. A classification is given of quasiprimitive permutation groups with a biregular dihedral subgroup. This is then used to characterize the family…

We explicitly determine all of the transitive groups of degree p-squared, p a prime, whose Sylow p-subgroup is not the wreath product of two cyclic groups of order p. Furthermore, we provide a general description of the transitive groups of…

Let $G$ be a permutation group, and denote with $\mu(G)$ and $b(G)$ its minimal degree and base size respectively. We show that for every $\varepsilon>0$, there exists a transitive permutation group $G$ of degree $n$ with \[ \mu(G)b(G) \geq…

Let us consider an abelian variety defined over $\mathbb{Q_{\ell}}$ with good supersingular reduction. In this paper we give explicit conditions that ensure that the action of the wild inertia group on the $\ell$-torsion points of the…

We study the density of periodic configurations for shift spaces defined on (the Cayley graph of) a finitely generated group. We prove that in the case of a full shift on a residually finite group and in that of a group shift space on an…

The appearance of so-called exceptional points in the complex spectra of non-Hermitian systems is often associated with phenomena that contradict our physical intuition. One example of particular interest is the state-exchange process…

Necessary and sufficient conditions for finite commutative semihypergroups to be built from abelian groups of the same order are established.