# Rendiconti del Seminario Matematico della Università di Padova

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**Volume 136, 2016, pp. 1–10**

**DOI: 10.4171/RSMUP/136-1**

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

Brendan McCann^{[1]}(1) Department of Mathematics and Computing, Waterford Institute of Technology, Main Campus Cork Road, Waterford, Ireland

In this note it is shown that if $G = AB$ 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.

*Keywords: *Products of groups, factorised groups, finite $p$-groups

McCann Brendan: 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), 1-10. doi: 10.4171/RSMUP/136-1