Article
| Title: | On products of prime element orders in finite groups (English) |
| Author: | Saha, Subhrajyoti |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 75 |
| Issue: | 2 |
| Year: | 2025 |
| Pages: | 437-444 |
| Summary lang: | English |
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| Category: | math |
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| 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 ${R_{*}}$. (English) |
| Keyword: | finite group |
| Keyword: | cyclic group |
| Keyword: | nilpotent group |
| Keyword: | element order |
| MSC: | 20B05 |
| MSC: | 20D60 |
| DOI: | 10.21136/CMJ.2025.0481-23 |
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| Date available: | 2025-05-20T11:43:16Z |
| Last updated: | 2025-05-26 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152951 |
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