Groups with some minimal conditions on non-nilpotent subgroups (Q2711632)

The article is dedicated to the study of locally graded groups with the minimal condition on non-nilpotent subgroups and locally finite groups with the weak minimal condition on non-nilpotent subgroups. For a non-locally finite locally graded group \(G\) with the minimal condition on non-nilpotent subgroups the authors prove its nilpotency (Theorem A). For a locally finite non-nilpotent non-Chernikov group \(G\) they prove the equivalence of the weak minimal condition on non-nilpotent subgroups of \(G\) to the following condition: there exists a prime \(p\) and a normal nilpotent \(p\)-subgroup \(K\) of \(G\) such that \(G/K\) is Chernikov and every non-nilpotent subgroup of \(G\) that has infinite rank contains \(K\) (Theorem B).