, Volume 99, Issue 5, pp 413-416
Date: 16 Nov 2012

A note on the size of the nilpotent residual in finite groups

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


In this note it is proved that \({|G : Z(G)| < |G^\prime| \cdot |G^\mathcal{N}|}\) if G is a finite non-abelian group with Φ (G) = 1.

This work was completed with the support of the National Natural Science Foundation of China (11071155) and the Discipline Project at the corresponding level of Shanghai (A.13-0101-12-005).