Czechoslovak Mathematical Journal, first online, pp. 1-8
On products of prime element orders in finite groups
Subhrajyoti Saha
Received November 1, 2023. Published online January 24, 2025.
Abstract: 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 $\nrs(G)$, which denotes the product of the prime element orders of a finite group $G$. We find a lower bound for $\nrs$ on the set of groups of the same order and deduce a result on nilpotent groups using $\nrs$.
Keywords: finite group; cyclic group; nilpotent group; element order
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Affiliations: Subhrajyoti Saha, University of Central Lancashire, Lancashire, PR1 2HE Preston, United Kingdom, e-mail: ssaha2@uclan.ac.uk
