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.
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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).
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Guo, X., Gong, L. A note on the size of the nilpotent residual in finite groups. Arch. Math. 99, 413–416 (2012). https://doi.org/10.1007/s00013-012-0452-5
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DOI: https://doi.org/10.1007/s00013-012-0452-5