A Sufficient Condition for Nilpotency of the Commutator Subgroup

Abstract

Let $G$ be a finite group with the property that if $a,b$ are commutators of coprime orders, then $|ab|=|a||b|$. We show that $G^{\prime }$ is nilpotent.

Cited by in corpus (4)

• A criterion for metanilpotency of a finite group
• A nilpotency criterion for some verbal subgroups
• Coprime commutators in finite groups
• $p$-nilpotency criteria for some verbal subgroups