On finite x-decomposable groups for X = {1, 2, 4} |
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| Authors: | X Guo J Li K P Shum |
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| Institution: | 1. Shanghai University, Shanghai, P. R. China
2. Institute of Mathematics, Yunnnan University, Kunming, P. R. China
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| Abstract: | A normal subgroup N of a finite group G is called an n-decomposable subgroup if N is a union of n distinct conjugacy classes of G. Each finite nonabelian nonperfect group is proved to be isomorphic to Q 12, or Z 2 × A 4, or G = ??a, b, c | a 11 = b 5 = c 2 = 1, b ?1 ab = a 4, c ?1 ac = a ?1, c ?1 bc = b ?1?? if every nontrivial normal subgroup is 2- or 4-decomposable. |
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