Products of Fitting Classes.
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 to express as semi-direct product of a divisible subgroup and some subgroup . We also apply the main Theorem to the -groups with center of index , for some prime . For these groups we compute the number of conjugacy classes and the number of abelian maximal subgroups and the number of nonabelian...
This article describes some properties of p-groups and some properties of commutative p-groups.
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).