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.
A property which ensures that a finitely generated hyper-(Abelian-by-finite) group is finite-by-nilpotent
Let be the class of groups satisfying the minimal condition on normal subgroups and let be the class of groups of finite lower central depth, that is groups such that for some positive integer . The main result states that if is a finitely generated hyper-(Abelian-by-finite) group such that for every , there exists a normal subgroup of finite index in satisfying for every , then is finite-by-nilpotent. As a consequence of this result, we prove that a finitely generated hyper-(Abelian-by-finite)...
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