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Paper   IPM / M / 7312
School of Mathematics
  Title:   On 5- and 6-decomposable finite groups
1.  A. R. Ashrafi
2.  Z. Yaoqing
  Status:   Published
  Journal: Math. Slovaca
  No.:  4
  Vol.:  53
  Year:  2003
  Pages:   373-383
  Supported by:  IPM
A finite group G is called n-decomposable if it is non-simple and each of its non-trivial proper normal subgroups is a union of n distinct conjugacy classes. In this paper, we investigate the structure of non-solvable non-perfect finite group G when G is 5- or 6-decomposable. We prove that G is 5-decomposable if and only if G is isomorphic with Z5×A5, A6.23 or Aut(PSL (2,q)) for q = 7,8. Also, G is 6-decomposable if and only if G is isomorphic with S6 or A6.22. Here, A6. 22 and A6. 23 are non-isomorphic split extensions of the alternating group A6, in the small group library of GAP [SCHONERT,M. et al.: GAP, Groups,Algorithms and Programming. Lehrstuhl für Mathematik, RWTH, Aachen, 1992].

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