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Groups whose finitely generated subgroups are either permutable or pronormal. (English) Zbl 1256.20038

In the theory of groups it is well-known that some families of subgroups can influence the structure of the whole group. For example, the structure of finite groups all whose subgroups are normal was completely described by R. Dedekind, and now such groups are known as Dedekind groups. Among different generalizations of normality there are more natural notions of pronormality and permutability. In the article under review, the authors study locally finite groups whose finitely generated subgroups are either permutable or pronormal and the structure of such groups is described in the main Theorem A of the article.

MSC:

20F50 Periodic groups; locally finite groups
20E07 Subgroup theorems; subgroup growth
20F19 Generalizations of solvable and nilpotent groups
20E15 Chains and lattices of subgroups, subnormal subgroups
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