Scholarlink

<p>We explicitly describe each unit of the group algebra <i>Z</i><sub><i>p</i></sub><i>S</i><sub>3</sub> for each positive prime <i>p</i> ≥ 5 by using a characterization of the group algebra of the metacyclic group <i>G</i>=<i>&lt;x, c</i> : <i>x</i><sup>3</sup>=1<i>, c</i><sup><i>n</i></sup>=1<i>, cxc</i><sup><i>–</i>1</sup>=<i>x</i><sup><i>–</i>1</sup><i>&gt;</i> over the finite field <i>F</i> of characteristic <i>p,</i> where <i>p</i> is a positive prime such that <i>p</i> ∤ 3<i>n.</i> Based on our findings, we pose a conjecture on the number of roots of some explicit polynomials over the prime field ℤ<sub><i>p</i></sub> for further academic explorations.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Units in the Group Algebra FS3

  • 期刊论文

  • 发表日期：

    2026年2月1日

查看全文
  • Abhinay Kumar Gupta,
  • R. K. Sharma

摘要

We explicitly describe each unit of the group algebra ZpS3 for each positive prime p ≥ 5 by using a characterization of the group algebra of the metacyclic group G=<x, c : x3=1, cn=1, cxc–1=x–1> over the finite field F of characteristic p, where p is a positive prime such that p ∤ 3n. Based on our findings, we pose a conjecture on the number of roots of some explicit polynomials over the prime field ℤp for further academic explorations.