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J. Korean Math. Soc. 2019; 56(3): 739-750
Online first article February 1, 2019 Printed May 1, 2019
https://doi.org/10.4134/JKMS.j180374
Copyright © The Korean Mathematical Society.
Finite $p$-groups all of whose subgroups of class 2 are generated by two elements
Pujin Li, Qinhai Zhang
Shanxi Normal University; Shanxi Normal University
We proved that finite $p$-groups in the title coincide with finite $p$-groups all of whose non-abelian subgroups are generated by two elements. Based on the result, finite $p$-groups all of whose subgroups of class 2 are minimal non-abelian (of the same order) are classified, respectively. Thus two questions posed by Berkovich are solved.
Keywords: finite $p$-groups, minimal non-abelian $p$-groups, subgroups of class 2
MSC numbers: 20D15, 20F05
Supported by: This work was supported by NSFC (nos.11471198, 11501045, 11771258).
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