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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/123/02/0239-0244

    • Keywords

       

      Conjugacy class sizes; primary; biprimary and triprimary elements; solvable groups; finite groups.

    • Abstract

       

      Let 𝐺 be a finite group and $G^∗$ be the set of primary, biprimary and triprimary elements of 𝐺. We prove that if the conjugacy class sizes of $G^∗$ are $\{1,m,n,mn\}$ with positive coprime integers 𝑚 and 𝑛,then 𝐺 is solvable. This extends a recent result of Kong (Manatsh. Math. 168(2)(2012) 267–271).

    • Author Affiliations

       

      Qinhui Jiang1 Changguo Shao1

      1. School of Mathematical Sciences, University of Jinan, Shandong 250022, China
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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