Commutators and commutator subgroups of finite $p$-groups

Abstract

We present a classification of finite $p$-groups $G$ with ${\gamma }_2(G)$, the commutator subgroup of $G$, of order $p^4$ and exponent $p$ such that not all elements of ${\gamma }_2(G)$ are commutators.

28 pages. Included the case $p=2$ and corrected some ambiguities