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| Paper IPM / M / 7312 |
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| Abstract: | |||||
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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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