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    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/124/01/0031-0036

    • Keywords

       

      Conjugacy class; rational group.

    • Abstract

       

      Let 𝐺 be a finite group and let $x^G$ denote the conjugacy class of an element 𝑥 of 𝐺. We classify all finite groups 𝐺 in the following three cases: (i) Each non-trivial conjugacy class of 𝐺 together with the identity element 1 is a subgroup of 𝐺, (ii) union of any two distinct non-trivial conjugacy classes of 𝐺 together with 1 is a subgroup of 𝐺, and (iii) union of any three distinct non-trivial conjugacy classes of 𝐺 together with 1 is a subgroup of 𝐺.

    • Author Affiliations

       

      Hemant Kalra1 Deepak Gumber1

      1. School of Mathematics and Computer Applications, Thapar University, Patiala 147 004, India

    • Dates

       
      Published
      February 2014
      Manuscript received
      29 August 2012
      Manuscript revised
      27 November 2012

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