Related papers: A theory of semiprimitive groups

Let $G$ be a finite primitive permutation group on a set $\Omega$ with nontrivial point stabilizer $G_{\alpha}$. We say that $G$ is extremely primitive if $G_{\alpha}$ acts primitively on each of its orbits in $\Omega \setminus \{\alpha\}$.…

This paper is about the structure of infinite primitive permutation groups and totally disconnected locally compact groups ("tdlc groups'"). The permutation groups we investigate are subdegree-finite (i.e. all orbits of point stabilisers…

We introduce a new class of transitive permutation groups which properly contains the automorphism groups of vertex-transitive graphs and digraphs. We then give a sufficient condition for a quotient of this family to remain in the family,…

We present a characterization of finite permutation groups which contain a transitive dihedral subgroup.

The concept of a k-translatable groupoid is explored in depth. Some properties of idempotent k-translatable groupoids, left cancellative k-translatable groupoids and left unitary k-translatable groupoids are proved. Necessary and sufficient…

We treat the problem of finding transitive subgroups G of S_n containing normal subgroups N_1 and N_2, with N_1 transitive and N_2 not transitive, such that G/N_1 is isomorphic G/N_2. We show that such G exist whenever n has a prime factor…

The thesis is devoted to abstract, geometric and symmetric aspects of modern elementary particle theories. A new direction in constructing supersymmetric and superstring models based on consequent and strong consideration and inclusion of…

A transitive simple subgroup of a finite symmetric group is very rarely contained in a full wreath product in product action. All such simple permutation groups are determined in this paper. This remarkable conclusion is reached after a…

A semigroup is completely simple if it has no proper ideals and contains a primitive idempotent. We say that a completely simple semigroup $S$ is a homogeneous completely simple semigroup if any isomorphism between finitely generated…

We give a constructive treatment of some basic concepts and results in semigroup theory. Focusing on semigroups equipped with an apartness relation, we give analogues, from the point of view of apartness, of several classical constructions…

Let $G$ be a group of collineations of a finite thick generalised quadrangle $\Gamma$. Suppose that $G$ acts primitively on the point set $\mathcal{P}$ of $\Gamma$, and transitively on the lines of $\Gamma$. We show that the primitive…

Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…

We investigate a smoothing property for strongly-continuous operator semigroups, akin to ultracontractivity in parabolic evolution equations. Specifically, we establish the stability of this property under certain relatively bounded…

Regular groups and fields are common generalizations of minimal and quasi-minimal groups and fields, so the conjectures that minimal or quasi-minimal fields are algebraically closed have their common generalization to the conjecture that…

A semi-projective representation is a homomorphism of a finite group into the group of semi-projective transformations of a finite dimensional vector space over a field. Schur's concept of a representation group for projective…

We give a complete characterization of countable primitive groups in several settings including linear groups, subgroups of mapping class groups, groups acting minimally on trees and convergence groups. The latter category includes as a…

We introduce the inverse monoid of inner partial automorphisms of a semigroup -- a tool that associates to every semigroup an inverse semigroup. When the semigroup is a group, this inverse semigroup is isomorphic to the group of inner…

We show that every quasitrivial n-ary semigroup is reducible to a binary semigroup, and we provide necessary and sufficient conditions for such a reduction to be unique. These results are then refined in the case of symmetric n-ary…

We introduce the quasi-ordinarization transform of a numerical semigroup. This transform will allow to organize all the semigroups of a given genus in a forest rooted at all quasi-ordinary semigroups with the given genus. This construction…

For a finite group acting on a polynomial ring, the Chevalley-Shephard-Todd Theorem proves that the fixed subring is isomorphic to a polynomial ring if and only if the group is generated by pseudo-reflections. In recent years, progress was…