Groups whose proper nonmaximal subgroups are cyclic or minimal noncyclic (Q2740354)

The author studies locally graded groups \(G\) such that every proper nonmaximal subgroup of \(G\) is either cyclic or minimal noncyclic (recall that a group \(G\) is called locally graded if every finitely generated (non-identity) subgroup contains a proper subgroup of finite index). Most groups from the list obtained are of the form \(G=A\leftthreetimes B\) where \(A\) is either cyclic or a direct sum of cyclic subgroups and \(B\) is either cyclic or a generalized quaternion group of small order. The main theorem of the work consists in the enumeration of 19 types of such groups. Note that the proof is shorter than the formulation.