5 papers · 1 filter
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…
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…
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…