A. V. Vasil'ev

activity

20142026

most citedOn recognition of symplectic and orthogonal groups of small dimensions by spectrum

7 citations · 14 across the 12 of their papers we have counts for

collaborators

Showing 2026 · math.GRShow all

4 papers · 2 filters

math.GR2026

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…

math.GR2026

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 $G$ , let $ω (G)$ be the set of element orders of $G$ and let $h (G)$ be the number of pairwise nonisomorphic finite groups $H$ with $ω (H) = ω (G)$ . We say that the re…

math.GR2026

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 $G$ having the same order and same set of conjugacy class sizes as an alternating or symmetric group $S$ must be isomorphic to $S$ . From thi…

math.GR2026

Recognition by element orders for simple linear and unitary groups

Maria A. Grechkoseeva, Alexey M. Staroletov, Andrey V. Vasil'ev

For a finite group $G$ , let $ω (G)$ be the set of element orders of $G$ and let $h (G)$ be the number of pairwise nonisomorphic finite groups $H$ with $ω (H) = ω (G)$ . We say that the re…