Units in the group algebra $FS_{3}$
Abstract
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.
Fields of Study & Subjects
Finite Group Theory Research
Advanced Topics in Algebra
Rings
Modules
and Algebras
Publication details
- Journal / source
- Ukrains’kyi Matematychnyi Zhurnal
- Volume
- 78
- Issue
- 1-2
- Pages
- 83–83
- Publication date
- 27 January 2026
- Language
- EN