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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...

Some questions on quasinilpotent groups and related classes.

M.J. Iranzo, J. Medina, F. Pérez-Monasor (2002)

Revista Matemática Iberoamericana

In this paper we will prove that if G is a finite group, X a subnormal subgroup of X F*(G) such that X F*(G) is quasinilpotent and Y is a quasinilpotent subgroup of NG(X), then Y F*(NG(X)) is quasinilpotent if and only if Y F*(G) is quasinilpotent. Also we will obtain that F*(G) controls its own fusion in G if and only if G = F*(G).

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