7 citations · 14 across the 12 of their papers we have counts for
12 papers
Arithmetic invariants for finite simple and related groups
Andrey V. Vasil'ev
In this short note, we address problems concerning the characterization of simple and related groups by various arithmetic invariants. We propose a uniform approach to such questio…
On the lengths of MDS codes with a two-transitive permutation automorphism group
Haihua Deng, Tao Feng, Andrey V. Vasil'ev
Let be an maximum distance separable (MDS) code with , and suppose that it has a -transitive permutation automorphism group. In this paper we show t…
The problem of recognition of finite simple groups by element orders is solved
Maria A. Grechkoseeva, Alexey M. Staroletov, Andrey V. Vasil'ev
For a finite group , let be the set of element orders of and let be the number of pairwise nonisomorphic finite groups with . We say that the re…
Characterization of the alternating and symmetric groups by the order and conjugacy class sizes
Ilya Gorshkov, Andrey V. Vasil'ev
We prove that an arbitrary finite group having the same order and same set of conjugacy class sizes as an alternating or symmetric group must be isomorphic to . From thi…
Recognition by element orders for simple linear and unitary groups
Maria A. Grechkoseeva, Alexey M. Staroletov, Andrey V. Vasil'ev
For a finite group , let be the set of element orders of and let be the number of pairwise nonisomorphic finite groups with . We say that the re…
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…
On finite groups isospectral to groups with abelian Sylow -subgroups
M. A. Grechkoseeva, A. V. Vasil'ev
The spectrum of a finite group is the set of orders of its elements. We are concerned with finite groups having the same spectrum as a direct product of nonabelian simple groups wi…
The structure of a finite group and the maximum -index of its elements
A-Ming Liu, Andrey V. Vasil'ev
Given a set of primes , the -index of an element of a finite group is the -part of the index of the centralizer of in . If is a singleton, we just…
On recognition of the direct squares of the simple groups with abelian Sylow 2-subgroups
Tao Li, A. R. Moghaddamfar, Andrey V. Vasil'ev +1
The spectrum of a group is the set of orders of its elements. Finite groups with the same spectra as the direct squares of the finite simple groups with abelian Sylow 2-subgroups a…
On recognition of direct powers of finite simple linear groups by spectrum
N. Yang, I. B. Gorshkov, A. M. Staroletov +1
The spectrum of a finite group is the set of its element orders. We give an affirmative answer to Problem 20.58(a) from the Kourovka Notebook proving that for every positive intege…
On recognition of symplectic and orthogonal groups of small dimensions by spectrum
M. A. Grechkoseeva, A. V. Vasil'ev, M. A. Zvezdina
We refer to the set of the orders of elements of a finite group as its spectrum and say that finite groups are isospectral if their spectra coincide. In the paper we determine all…
Almost recognizability by spectrum of simple exceptional groups of Lie type
Andrey V. Vasil'ev, Alexey M. Staroletov
The spectrum of a finite group is the set of its elements orders. Groups are said to be isospectral if their spectra coincide. For every finite simple exceptional group ,…