• On finite groups whose every proper normal subgroup is a union of a given number of conjugacy classes

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/114/03/0217-0224

    • Keywords

       

      Finite group; -decomposable subgroup; conjugacy class; -decomposable group

    • Abstract

       

      Let G be a finite group andA be a normal subgroup ofG. We denote by ncc(A) the number ofG-conjugacy classes ofA andA is calledn-decomposable, if ncc(A)= n. SetKG = {ncc(A)¦A ⊲ G}. LetX be a non-empty subset of positive integers. A groupG is calledX-decomposable, ifKG =X.

      Ashrafi and his co-authors [1-5] have characterized theX-decomposable non-perfect finite groups forX = {1, n} andn ≤ 10. In this paper, we continue this problem and investigate the structure ofX-decomposable non-perfect finite groups, forX = {1, 2, 3}. We prove that such a group is isomorphic to Z6, D8, Q8, S4, SmallGroup(20, 3), SmallGroup(24, 3), where SmallGroup(m, n) denotes the mth group of ordern in the small group library of GAP [11].

    • Author Affiliations

       

      Ali Reza Ashrafi1 Geetha Venkataraman1 2

      1. Department of Mathematics, University of Kashan, Kashan, Iran
      2. Department of Mathematics and Mathematical Sciences Foundation, St. Stephen’s College, Delhi - 110 007, India
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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