On group characterization by numbers of conjugate classes-Reference-Cited by-同舟云学术

On group characterization by numbers of conjugate classes

Published:2023-03-23 Issue:3-4 Volume:28 Page:18-25
ISSN:2712-8954
Container-title:Vestnik of Samara University. Natural Science Series
language:
Short-container-title:Vestnik of Samara University. Natural Science Series

Author:

Voskresenskaya Galina V.^ORCID

Abstract

Let c(n,G) be a number of conjugate elements of order n in a group G.In the article we study the problem of recognition of finite group by the set ncl(G) that consists of numbers c(n,G). We prove that Abelian groups can be recognized by the set ncl(G) when the order of the group is known. We also describe some other types of groups that can be recognized. The examples of non-isomorphic groups with the same sets ncl(G) are given. Some theorems about a group recognition by partial conditions on c(n,G). are proved.

Publisher

Samara National Research University

Subject

General Medicine

Reference11 articles.

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3. Voskresenskaya G.V. Group recognition by conditions on classes of conjugate elements. In: Eighth school-conference "Lie algebras, algebraic groups and the theory of invariants". Abstracts. Мoscow: MTsNMO, 2020, p. 19. (In Russ.)

4. Recognizability of Symmetric Groups by Spectrum

5. Finite Almost Simple Groups Whose Gruenberg–Kegel Graphs Coincide with Gruenberg–Kegel Graphs of Solvable Groups