1 citations · 3 across the 10 of their papers we have counts for
10 papers
Relatively closed subgroups of permutation groups with a cyclic regular normal subgroup
Alexander Buturlakin, Andrey V. Vasil'ev
Motivated by some known problems concerning combinatorial structures associated with finite one-dimensional affine permutation groups, we study subgroups which are closed in $\oper…
Equationally separable classes of groups
Alexander Buturlakin, Anton Klyachko, Denis Osin
Over each nontrivial finite group , there exists a finite system of equations having no solutions in larger finite groups but having a solution in a periodic group containing $G…
The spectra of almost simple groups with socle
Alexander A. Buturlakin, Maria A. Grechkoseeva
We give an explicit description of the set of element orders for every almost simple group with socle .
The time complexity of some algorithms for generating the spectra of finite simple groups
Alexander Buturlakin
The spectrum is the set of orders of elements of . We consider the problem of generating the spectrum of a finite nonabelian simple group given by the degree of i…
Area of a triangle and angle bisectors
A. A. Buturlakin, S. S. Presnyakov, D. O. Revin +1
Consider a triangle with given lengths of its internal angle bisectors. We prove that in general, it is impossible to construct a square of the same area as $AB…
The graph of atomic divisors and constructive recognition of finite simple groups
Alexander A. Buturlakin, Andrey V. Vasil'ev
The spectrum of a finite group is the set of orders of elements of . We present a polynomial-time algorithm that, given a finite set of positive integers…
A Criterion for the Existence of a Solvable -Hall Subgroup in a Finite Group
A. A. Buturlakin, A. P. Khramova
Let be a finite group and let be a set of primes. In this paper, we prove a criterion for the existence of a solvable -Hall subgroup of , precisely, the group has…
Locally finite groups of finite -dimension
A. A. Buturlakin
The supremum of lengths of strict chains of nested centralizers is called the -dimension (centralizer dimension) of . We prove two structure theorems for locally finite group…
Groups with bounded centralizer chains and the~Borovik--Khukhro conjecture
Alexander Buturlakin, Danila Revin, Andrey Vasil'ev
Let be a locally finite group and the Hirsch--Plotkin radical of . Denote by the full inverse image of the generalized Fitting subgroup of in . Assume…
Spectra of finite symplectic and orthogonal groups
A. A. Buturlakin
The spectra of a finite group is the set of its element orders. We obtain an arithmetic description of finite symplectic and orthogonal groups. In particular, a description of spec…