Groups with all proper subgroups (finite rank)-by-nilpotent
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Let G be a group in which every proper subgroup is an extension of a group of finite (Prüfer) rank by a nilpotent group of class at most c. We show that if G is locally soluble-by-finite, then G is an extension of a group of finite rank by a nilpotent group of class at most c. This result is extended to cover groups G that belong to a certain extensive class \(\frak X \) of locally graded groups.
KeywordsNilpotent Group Proper Subgroup Finite Rank Extensive Class
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