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Algebra Logika, 2023 Volume 62, Number 1, Pages 76–92 (Mi al2748)

Finite 4-primary groups with disconnected Gruenberg–Kegel graph containig a triangle

A. S. Kondrat'evab

a Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
b N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg

Abstract: We give a description of finite 4-primary groups with disconnected Gruenberg–Kegel graph containing a triangle. As a corollary, finite groups whose Gruenberg–Kegel graph coincides with the Gruenberg–Kegel graph of $^3D_4(2)$ are exemplified, which generalizes V. D. Mazurov' description of finite groups isospectral to the group $^3D_4(2)$.

Keywords: finite group, 4-primary group, chief factor, Gruenberg–Kegel graph (prime graph), Brauer character.

UDC: 512.542

Received: 24.05.2022
Revised: 30.10.2023

DOI: 10.33048/alglog.2023.62.105



© Steklov Math. Inst. of RAS, 2024