2000 Mathematics Subject Classification: 20F16, 20E15. Groups in which every contranormal subgroup is normally complemented has been considered. The description of such groups G with the condition Max-n and such groups having an abelian nilpotent residual satisfying Min-G have been obtained.
In questo lavoro studiamo i non CC-gruppi monolitici con tutti i quozienti propri CC-gruppi, che hanno sottogruppi abeliani normali non banali.
Let be a field, be a vector space over , be the group of all automorphisms of the vector space . A subspace is called almost -invariant, if is finite. In the current article, we begin the study of those subgroups of for which every subspace of is almost -invariant. More precisely, we consider the case when is a periodic group. We prove that in this case includes a -invariant subspace of finite codimension whose subspaces are -invariant.
The current article considers some infinite groups whose finitely generated subgroups are either permutable or pronormal. A group is called a generalized radical, if has an ascending series whose factors are locally nilpotent or locally finite. The class of locally generalized radical groups is quite wide. For instance, it includes all locally finite, locally soluble, and almost locally soluble groups. The main result of this paper is the followingTheorem. Let be a locally generalized radical...
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