M. Grechkoseeva

activity

20212026

most citedFinite groups isospectral to simple groups

15 citations · 19 across the 7 of their papers we have counts for

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7 papers · 1 filter

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

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…

math.GR2026

On recognition of simple classical groups with prime graph independence number $4$ by spectrum

Maria A. Grechkoseeva, Vladislav M. Rodionov

Let $L$ be one of the finite simple classical groups $L_{8} (q)$ , $U_{8} (q)$ , $O_{10}^{+} (q)$ , $O_{10}^{-} (q)$ or $O_{12}^{+} (q)$ , with $q$ odd. We prove that every finite group having the sa…

math.GR2025

On primitive prime divisors of the orders of Suzuki-Ree groups (corrected version)

Maria Grechkoseeva

There is a well-known factorization of the number $2^{2 m} + 1$ , with $m$ odd, related to the orders of tori of simple Suzuki groups: $2^{2 m} + 1$ is a product of $a = 2^{m} + 2^{(m + 1) /2} + 1$ …

math.GR2023

The spectra of almost simple groups with socle $E_{7} (q)$

Alexander A. Buturlakin, Maria A. Grechkoseeva

We give an explicit description of the set of element orders for every almost simple group with socle $E_{7} (q)$ .

math.GR2021★ 15 cited

Finite groups isospectral to simple groups

Maria A. Grechkoseeva, Victor D. Mazurov, Wujie Shi +2

The spectrum of a finite group is the set of element orders of this group. The main goal of this paper is to survey results concerning recognition of finite simple groups by spectr…

math.GR2021★ 4 cited

On the prime graph of a finite group with unique nonabelian composition factor

Maria A. Grechkoseeva, Andrey V. Vasil'ev

We say that finite groups are isospectral if they have the same sets of orders of elements. It is known that every nonsolvable finite group $G$ isospectral to a finite simple group…

The problem of recognition of finite simple groups by element orders is solved

Recognition by element orders for simple linear and unitary groups

On recognition of simple classical groups with prime graph independence number 4 by spectrum

On primitive prime divisors of the orders of Suzuki-Ree groups (corrected version)

The spectra of almost simple groups with socle E7​(q)

Finite groups isospectral to simple groups

On the prime graph of a finite group with unique nonabelian composition factor

On recognition of simple classical groups with prime graph independence number $4$ by spectrum

The spectra of almost simple groups with socle $E_{7} (q)$