Finite $p$-groups all of whose subgroups of class 2 are generated by two elements
J. Korean Math. Soc. 2019 Vol. 56, No. 3, 739-750
Published online May 1, 2019
Pujin Li, Qinhai Zhang
Shanxi Normal University; Shanxi Normal University
Abstract : 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
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