A. Staroletov

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

math.GR2025

On eigenvalues of permutations in irreducible representations of symmetric and alternating groups

Alexey Staroletov

Denote the symmetric group of degree $n$ by $S_{n}$ . Let $I ¨ $ be an irreducible representation of $S_{n}$ over the field of complex numbers and $I ¨ \in S_{n}$ . In this paper, we describe…