2025/107/1-2 (5)
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DOI: 10.5486/PMD.2025.9948
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pp. 107-114
The size of the class 2 residual in finite groups
Authors:
Lü Gong 
, Ziru Jing and Baojun Li
Abstract:
Let $G^c$ be the class 2 residual of a finite group $G$. In this paper, it is proved that $|G:Z(G)|＜|G^{c}|^2$ if $G$ is a finite non-abelian group with $\Phi(G)=1$.
Keywords: finite group, commutator subgroup, nilpotent residual, class 2 residual, Fitting subgroup
Mathematics Subject Classification: 20D10, 20D20