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Bull. Korean Math. Soc. 2022; 59(4): 951-960

Published online July 31, 2022 https://doi.org/10.4134/BKMS.b210562

Copyright © The Korean Mathematical Society.

A generalization of ${\mathcal A}_2$-groups

Junqiang Zhang

Shanxi Normal University

Abstract

In this paper, we determine the finite $p$-group such that the intersection of its any two distinct minimal nonabelian subgroups is a maximal subgroup of the two minimal nonabelian subgroups, and the finite $p$-group in which any two distinct ${\mathcal A}_1$-subgroups generate an ${\mathcal A}_2$-subgroup. As a byproduct, we answer a problem proposed by Berkovich and Janko.

Keywords: Finite $p$-groups, minimal nonabelian subgroups, maximal subgroups

MSC numbers: Primary 20D15

Supported by: This work was financially supported by NSFC (No. 11771258 \& 11971280).

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