A. Staroletov

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20182026

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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 $ω (G)$ 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.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 $ρ$ be an irreducible representation of $S_{n}$ over the field of complex numbers and $σ \in S_{n}$ . In this paper, we describe th…

math.GR2019

The minimal polynomials of powers of cycles in the ordinary representations of symmetric and alternating groups

Nanying Yang, Alexey Staroletov

Denote the alternating and symmetric groups of degree $n$ by $A_{n}$ and $S_{n}$ respectively. Consider a permutation $σ \in S_{n}$ all of whose nontrivial cycles are of the same length.…

math.GR2018

Minimal 3-generated Majorana algebras

Andrey Mamontov, Alexey Staroletov, Madeleine Whybrow

Majorana theory was introduced by A. A. Ivanov as the axiomatization of certain properties of the 2A-axes of the Griess algebra. Since its inception, Majorana theory has proved to…

math.GR2018

On groups having the prime graph as alternating and symmetric groups

Ilya Gorshkov, Alexey Staroletov

The {\it prime graph} $Γ (G)$ of a finite group $G$ is the graph whose vertex set is the set of prime divisors of $∣ G ∣$ and in which two distinct vertices $r$ and $s$ are adjacent i…