Locally soluble groups with all nontrivial normal subgroups isomorphic (Q1344472)

In a previous article [J. Pure Appl. Algebra 88, 169-171 (1993; Zbl 0797.20027)] the authors conjectured that, if \(G\) is a finitely generated infinite group which is isomorphic to all its non-trivial normal subgroups, then either \(G\) is simple or cyclic. Here they prove that this conjecture is true, provided that \(G\) is locally soluble and \(G/G'\) has finite \(p\)-rank for \(p = 0\) or a prime.