On finite $p$-groups that are the product of a subgroup of class two and an abelian subgroup of order $p^3$

Brendan McCann

doi:10.4171/rsmup/136-1

JournalsrsmupVol. 136pp. 1–10

On finite $p$ -groups that are the product of a subgroup of class two and an abelian subgroup of order $p^{3}$

Brendan McCann
Waterford Institute of Technology, Ireland

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Abstract

In this note it is shown that if $G = A B$ is a finite $p$ -group that is the product of an abelian subgroup $A$ of order $p^{3}$ and a subgroup $B$ of nilpotency class two, then $G$ can have derived length at most three.

Cite this article

Brendan McCann, On finite $p$ -groups that are the product of a subgroup of class two and an abelian subgroup of order $p^{3}$ . Rend. Sem. Mat. Univ. Padova 136 (2016), pp. 1–10

DOI 10.4171/RSMUP/136-1