arXiv subjects

Alexander Buturlakin

Publications and source records attributed to Alexander Buturlakin.

4 recordsLinked to original sources

arXiv2025

Relatively closed subgroups of permutation groups with a cyclic regular normal subgroup

Motivated by some known problems concerning combinatorial structures associated with finite one-dimensional affine permutation groups, we study subgroups which are closed in $\operatorname{\Gamma{L}}_1(q)$. This brings us to a description of the relatively closed subgroups of permutation groups with a cyclic regular normal subgroup. Our results, in particular, provide a classification of the minimal nontrivial one-dimensional affine association schemes which generalizes the recent Muzychuk classification of the one-dimensional affine rank 3 graphs.

math.GR↗

arXiv2025

Equationally separable classes of groups

Over each nontrivial finite group $G$, there exists a finite system of equations having no solutions in larger finite groups but having a solution in a periodic group containing $G$. We prove several similar facts about amenable, orderable, locally indicable, solvable, nilpotent, and other classes of groups. As a byproduct, we also show that any amalgam of two countable periodic groups with finite intersection embeds into a periodic group, thereby answering a 1960 question of B. Neumann in the countable case.

math.GR↗

arXiv2021

The time complexity of some algorithms for generating the spectra of finite simple groups

The spectrum $\omega(G)$ is the set of orders of elements of $G$. We consider the problem of generating the spectrum of a finite nonabelian simple group $G$ given by the degree of $G$ if $G$ is an alternating group, or the Lie type, Lie rank and order of the underlying field if $G$ is a group of Lie type.

math.GR↗

arXiv2017

Groups with bounded centralizer chains and the~Borovik--Khukhro conjecture

Let $G$ be a locally finite group and $F(G)$ the Hirsch--Plotkin radical of $G$. Denote by $S$ the full inverse image of the generalized Fitting subgroup of $G/F(G)$ in $G$. Assume that there is a number $k$ such that the length of every chain of nested centralizers in $G$ does not exceed $k$. The Borovik--Khukhro conjecture states, in particular, that under this assumption the quotient $G/S$ contains an abelian subgroup of index bounded in terms of $k$. We disprove this statement and prove some its weaker analog.

math.GR↗