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Locally nilpotent $$p$$-groups whose proper subgroups are hypercentral or nilpotent-by-Chernikov. (English) Zbl 0961.20031
The author’s four main results are the following. (1) Let $$G$$ be a non-hypercentral Fitting $$p$$-group such that every proper subgroup of $$G$$ is hypercentral and soluble. Then $$G$$ is soluble. (2) Let $$G$$ be a barely transitive locally nilpotent $$p$$-group. If a point stabilizer of $$G$$ is hypercentral and soluble, then $$G$$ is not perfect. (3) Let $$G$$ be a locally nilpotent $$p$$-group with each of its proper subgroups nilpotent-by-Chernikov. Then $$G$$ is nilpotent-by-Chernikov. (4) Let $$G$$ be a locally nilpotent $$p$$-group with each of its proper subgroups nilpotent-by-finite. If $$G$$ is not nilpotent-by-finite, then $$G$$ modulo its derived subgroup is a Prüfer $$p^\infty$$-group.

##### MSC:
 20F19 Generalizations of solvable and nilpotent groups 20F50 Periodic groups; locally finite groups 20E07 Subgroup theorems; subgroup growth
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