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    • Normalized unit groups and their conjugacy classes

      S KAUR M KHAN

      Research Article Volume 130 Published: 10 January 2020 Article ID 0007

    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/130/0007

    • Keywords

       

      Group ring; unitary subgroup; unit group; conjugacy class

    • Abstract

       

      Let $G = H \times A$ be a finite 2-group, where $H$ is a non-abelian group of order 8 and $A$ is an elementary abelian 2-group. We obtain a normal complement of $G$ in the normalized unit group $V(FG)$ and in the unitary subgroup $V_{\ast}(FG)$ over the field $F$ with 2 elements. Further, for a finite field $F$ of characteristic 2, we derive class size of elements of $V(FG)$. Moreover, we provide class representatives of $V_{\ast}(FH)$.

    • Author Affiliations

       

      S KAUR1 M KHAN1

      1. Department of Mathematics, Indian Institute of Technology Ropar, Nangal Road, Rupnagar 140 001, India

    • Dates

       
      Published
      10 January 2020
      Manuscript received
      8 May 2018
      Manuscript revised
      15 March 2019
      Accepted
      31 May 2019
      Early published
      Unedited version published online
      Final version published online
      9 January 2020

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