8 papers · 1 filter
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 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…