6 papers
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…
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…