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IPM
30
YEARS OLD

“School of Mathematics”

Paper   IPM / M / 750
   School of Mathematics
  Title: On finite groups whose every normal subgroups is a union of the same number of conjugacy classes
  Author(s):
1 . A. R. Ashrafi
2 . H. Sahraei
  Status: Published
  Journal: Vietnam J. Math.
  No.: 3
  Vol.: 30
  Year: 2002
  Pages: 289-294
  Supported by: IPM
  Abstract:
Let G be a finite group and NG denote the set of non-trivial proper normal subgroups of G. An element K of NG is said to be n-decomposable if K is a union of n distinct conjugacy classes of G.
In this paper, we investigate the structure of finite groups G in which G′ is a union of three distinct conjugacy classes of G. We prove, under certain conditions, G is a Frobenius group with kernel G′ and its complement is abelian. Furthermore, we investigate the structure of finite groups G in which NG ≠ ∅ and every element of NG is n-decomposable, for a given n. When G is solvable or n=2,3,4, we determine the structure of such groups.

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