The Fitting Subgroup and Some Injectors of Radical Locally Finite Groups with min-pfor Allp

On products of generalized nilpotent groups

“…By [4, Theorem 3], we have that B 2 is a cL-formation and by [5,Corollary 2] if G is a cL-group such that G=mðGÞ A B 2 , then G A B 2 . The same is true for the class ðLNÞ 2 (see [8, (6. …”

“…This paper deals with groups belonging to the class cL of all radical locally finite groups with min-p for all primes p. More precisely, we study cL-groups G ¼ AB which are the product of two subgroups A and B belonging to the class B of all cL-groups in which each proper subgroup has a proper normal closure. The class B has been introduced and studied in [4,5]. The results of these papers show that this class is intermediate between nilpotent and locally nilpotent groups, and that it is the natural generalization of the class of finite nilpotent groups from the finite universe to the universe cL.…”

On a class of locally finite T-groups

“…It has been studied extensively in [1,2,3]. This class is intermediate between nilpotent and locally nilpotent groups, and it is the natural generalisation of the class of finite nilpotent groups from the finite universe to the universe cL.…”

A class of generalized supersoluble groups

“…The class B has been introduced and studied in [3], [4]. The results of these papers show that this class is intermediate between nilpotent and locally nilpotent groups, and that it is the natural generalization of the class of finite nilpotent groups from the finite universe to the universe cL.…”