The life and mathematics of Ismail Mohamed

Abstract

Ismail Mohamed’s major contributions, which were in collaboration with Hermann Heineken, was to provide a procedure for constructing groups with prescribed characteristics. In particular, they constructed examples of non-nilpotent groups in which every subgroup is subnormal and nilpotent. These have become known as the Heineken–Mohamed groups. This construction led to settling a few questions posed, in the 1940s, by Kurosh and Cernikov in their survey of various generalisations of nilpotency. He also studied properties of series of subgroups of a group G that are constructed from arbitrary subgroups of automorphisms of a group.