Finite Non-solvable Groups Without Elements of Order 10

Abstract

As main result of the paper, we describe finite non-solvable groups without elements of order 10. In addition, we prove a new general structural theorem on finite non-solvable groups without elements of order 2p for an odd prime p. The theorem reinforces essentially the well-known Vasil’ev theorem on these groups and can be applied to obtain new arithmetical characterizations of finite groups.

Keywords

Finite group / Non-solvable group / Gruenberg–Kegel graph / 20D05 / 20D60 / 05C25

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Funding

National Natural Science Foundation of China(12171126)

Fundamental Research Funds for Central Universities-President’s Fund((JUS RP202406006)

RIGHTS & PERMISSIONS

School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature