A criterion for metanilpotency of a finite group

Abstract

We prove that the $k$th term of the lower central series of a finite group $G$ is nilpotent if and only if $|ab|=|a||b|$ for any ${\gamma }_k$-commutators $a,b\in G$ of coprime orders.

References in corpus (2)

• A Sufficient Condition for Nilpotency of the Commutator Subgroup
• A Sufficient Condition for Nilpotency in a Finite Group

Cited by in corpus (3)

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