• Finite Groups with Three Conjugacy Class Sizes of some Elements

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    • Keywords


      Conjugacy class sizes; 𝑝-nilpotent groups; finite groups.

    • Abstract


      Let 𝐺 be a finite group. We prove as follows: Let 𝐺 be a 𝑝-solvable group for a fixed prime 𝑝. If the conjugacy class sizes of all elements of primary and biprimary orders of 𝐺 are $\{1,p^a,n\}$ with 𝑎 and 𝑛 two positive integers and $(p,n)=1$, then 𝐺 is 𝑝-nilpotent or 𝐺 has abelian Sylow 𝑝-subgroups.

    • Author Affiliations


      Qingjun Kong1

      1. Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, People’s Republic of China
    • Dates

  • Proceedings – Mathematical Sciences | News

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      Posted on July 25, 2019

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