A NOTE ON STRONGLY PERFECT GROUPS

J. Goswami

  DOI:  https://doi.org/10.37418/amsj.9.11.97

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In this work, we have introduced the notion of strongly perfect group. Let $G$ be a finite group and $\delta(G) = \sum_{H \leq G}|H|$ be the sum of the orders of the subgroups of $G$. We define $G$ to be strongly perfect if $\delta(G) = 2|G|$. Clearly, this group is a generalization of perfect group introduced by Leinster [1]. We have investigated some properties of this group.

Keywords: Perfect number, Abelian group, cyclic group, strongly perfect group.