Centre-by-metabelian groups with a condition on infinite subsets.
Groups whose proper subgroups are Baer-by-Chernikov or Baer-by-(finite rank)
Our main result is that a locally graded group whose proper subgroups are Baer-by-Chernikov is itself Baer-by-Chernikov. We prove also that a locally (soluble-by-finite) group whose proper subgroups are Baer-by-(finite rank) is itself Baer-by-(finite rank) if either it is locally of finite rank but not locally finite or it has no infinite simple images.
A note on torsion-by-nilpotent groups
On certain characterizations of barely transitive groups
On minimal non--groups
A group is said to be a -group, if is a polycyclic-by-finite group for all . A minimal non--group is a group which is not a -group but all of whose proper subgroups are -groups. Our main result is that a minimal non--group having a non-trivial finite factor group is a finite cyclic extension of a divisible abelian group of finite rank.
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