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Keywords:
finite group; cyclic group; nilpotent group; element order
finite group; cyclic group; nilpotent group; element order
Summary:
Let $G$ be a finite group. The functions $\psi (G)$ and $\psi _{*}(G)$ denote the sum of the element orders and the sum of the prime element orders of $G$, respectively. Significant results related to the study of these functions have been published recently. Further, the function $R(G)$ was introduced to denote the product of the element orders of $G$. We introduce ${R_{*}}(G)$, which denotes the product of the prime element orders of a finite group $G$. We find a lower bound for ${R_{*}}$ on the set of groups of the same order and deduce a result on nilpotent groups using ${R_{*}}$.
References:
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