Units in the group algebra $FS_{3}$
UDC 512.552 We explicitly describe each unit of a group algebra $Z_{p} S_{3}$ for each positive prime $p \geq 5$ by using a characterization of the group algebra of the metacyclic group $G= \langle x,c\colon x^{3}=1,\ c^{n}=1,\ cxc^{-1 } = x^{-1} \rangle$ over the finite field $F$ of characteristic...
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| Date: | 2026 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2026
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/9213 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 512.552
We explicitly describe each unit of a group algebra $Z_{p} S_{3}$ for each positive prime $p \geq 5$ by using a characterization of the group algebra of the metacyclic group $G= \langle x,c\colon x^{3}=1,\ c^{n}=1,\ cxc^{-1 } = x^{-1} \rangle$ over the finite field $F$ of characteristic $p,$ where $p$ is a positive prime such that $p \nmid 3n.$ Based on our findings, we pose a conjecture on the number of roots of some explicit polynomials over the prime field $\mathbb{Z}_{p}$ for further academic explorations. |
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| DOI: | 10.3842/umzh.v78i1-2.9213 |