Related papers: Classifications of quasitrivial semigroups

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 develop a general approach to the study of maximal nilpotent subsemigroups of finite semigroups. This approach can be used to recover many known classifications of maximal nilpotent subsemigroups, in particular, for the symmetric inverse…

Coclass theory has been a highly successful approach towards the investigation and classification of finite nilpotent groups. Here we suggest a similar approach for finite nilpotent semigroups. This differs from the group theory setting in…

The authors investigate the structure of quasi-o-minimal groups. Among other results, they show that quasi-o-minimal groups are abelian, that quasi-o-minimal densely ordered archimedian groups are divisible, and that every divisible…

We study varieties of semigroups related to completely 0-simple semigroup. We present here an algorithmic descriptions of these varieties interms of "forbidden" semigroups.

Abelian groups having partial orderings compatible with their binary operations have long been studied in the literature. In particular, lattice-ordered abelian groups constitute a universal-algebraic variety, and thus form a category which…

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 investigate simple endotrivial modules of finite quasi-simple groups and classify them in several important cases. This is motivated by a recent result of Robinson showing that simple endotrivial modules of most groups come from…

Quasigroup equational definitions are given.

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…

We introduce the notion of semigroup with a tight ideal series and investigate their closures in semitopological semigroups, particularly inverse semigroups with continuous inversion. As a corollary we show that the symmetric inverse…

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 study finite semiprimitive permutation groups, that is, groups in which each normal subgroup is transitive or semiregular. We give bounds on the order, base size, minimal degree, fixity, and chief length of an arbitrary…

We consider the growth, order, and finiteness problems for automaton (semi)groups. We propose new implementations and compare them with the existing ones. As a result of extensive experimentations, we propose some conjectures on the order…

In this article we introduce and study a class of finite groups for which the orders of normal subgroups satisfy a certain inequality. It is closely connected to some well-known arithmetic classes of natural numbers.

We define quasi-Frobenius semigroups and find necessary and sufficient conditions under which a semigroup algebra of a 0-cancellative semigroup is quasi-Frobenius.

The article is devoted to linear quasigroups and some of their generalizations. In the first part main definitions and notions of the theory of quasigroups are given. In the second part some elementary properties of linear quasigroups and…

We consider groups of finite Morley rank with solvable local subgroups of even and mixed types. We also consider miscellaneous aspects of small groups of finite Morley rank of odd type.

We generalize the idea of a Schur ring of a group to the category of semigroups. Fundamental results of Schur rings over groups are shown to be true for Schur rings over semigroups. Examples where Schur rings differ between the two…

We classify quasi-simple finite groups of essential dimension 3.