Let G be a group with the property that there are no infinite descending chains of non-subnormal subgroups of G for which all successive indices are infinite. The main result is that if G is a locally (soluble-by-finite) group with this property then either G has all subgroups subnormal or G is a soluble-by-finite minimax group. This result fills a gap left in an earlier paper by the same autho...

Let C be a class of groups, closed under taking subgroups and quotients. We prove that if all metabelian groups of C are torsion-by-nilpotent, then all soluble groups of C are torsion-by-nilpotent. From that, we deduce the following consequence, similar to a well-known result of P. Hall: if H is a normal subgroup of a group G such that H and G/H ′ are (locally finite)-by-nilpotent, then G is (l...

We obtain a number of consequences of the theorem on the automatic continuity of locally bounded finite-dimensional representations of connected Lie groups on the derived subgroup of the group, as well as an analogue of Lie’s theorem for (not necessarily continuous) finite-dimensional representations of connected soluble locally compact groups. In particular, we give a description of connected ...

Assistant Professor, Department of Surgical Oncology, Acharya Tulsi Regional Cancer Treatment & Research Centre, Bikaner Consulting Oncosurgeon, Department of Surgical Oncology, Saviour Multispecialty Hospital, Ahmedabad Retd.Professor & Chief of Surgical Oncology, Department of Surgical Oncology, Gujarat Cancer & Research Institute, Ahmedabad Plastic Surgeon, Department of Surgical Oncology, G...