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Properties of subgroups not containing their centralizers

Lemnouar Noui — 2009

Annales mathématiques Blaise Pascal

In this paper, we give a generalization of Baer Theorem on the injective property of divisible abelian groups. As consequences of the obtained result we find a sufficient condition for a group G to express as semi-direct product of a divisible subgroup D and some subgroup H . We also apply the main Theorem to the p -groups with center of index p 2 , for some prime p . For these groups we compute N c ( G ) the number of conjugacy classes and N a the number of abelian maximal subgroups and N n a the number of nonabelian...

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