A Gaschütz–Lubeseder Type Theorem in a Class of Locally Finite Groups

A class of generalized supersoluble groups

“…Then G/M G is either a finite soluble primitive group, if M is a maximal subgroup of G, or a semiprimitive group, if M is not maximal in G (here, a group G is said to be semiprimitive if it is the split extension, G = [D]M , of a faithful divisibly irreducible ZM -module D by a finite soluble group M ). This result, proved in [2], confirms the importance of major subgroups in the study of the structure of groups and motivates some definitions which are in some sense extensions of well known ones in the finite universe. Definition 1.…”

A local approach to a class of locally finite groups

“…Let U be a subgroup of a group G and consider the properly ascending chains U = U 0 <U 1 Then we define fj,(G) to be the intersection of all major subgroups of G.…”