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<p>Let <i>G</i> be a finite group. The functions <i>ψ</i>(<i>G</i>) and <i>ψ</i><sub>*</sub>(<i>G</i>) denote the sum of the element orders and the sum of the prime element orders of <i>G</i>, respectively. Significant results related to the study of these functions have been published recently. Further, the function <i>R</i>(<i>G</i>) was introduced to denote the product of the element orders of <i>G</i>. We introduce <i>R</i><sub>*</sub>(<i>G</i>), which denotes the product of the prime element orders of a finite group <i>G</i>. We find a lower bound for <i>R</i><sub>*</sub> on the set of groups of the same order and deduce a result on nilpotent groups using <i>R</i><sub>*</sub>.</p>

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On products of prime element orders in finite groups

  • 期刊论文

  • 发表日期：

    2025年1月24日

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  • Subhrajyoti Saha

摘要

Let G be a finite group. The functions ψ(G) and ψ*(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*.