, Volume 99, Issue 5, pp 413-416

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

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Abstract

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).