Finite p-Groups G with H'=G' for Each A₂-Subgroup H

ALGEBRA COLLOQUIUM（2023）

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摘要

A finite p-group G is called an At-group if tis the minimal non-negative integer such that all subgroups of index pt of G are abelian. The finite p-groups G with H'=G' for all A(2)-subgroups H of Gare classified completely in this paper. As an application, a problem proposed by Berkovich is solved.

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finite p-group, minimal non-abelian subgroup, A(2)-subgroup, derived sub-group

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Finite p-Groups G with H'=G' for Each A2-Subgroup H

Finite p-Groups G with H'=G' for Each A₂-Subgroup H