Tim Wall

Tim Wall, the Australian group theorist, died at the weekend, at the age of 98. His name was Gordon Elliott Wall; he was always known as Tim, after an Australian cricketer of the same name.

He is possibly most famous for his bold conjecture that the number of maximal subgroups of a group is less than the order of the group. After decades of research, the conjecture was disproved, but it is “almost” true, and holds for many special types of group. The essence of a good conjecture.

The Road Closure Conjecture has been on my mind lately; as noted here, a generalisation of the conjecture asserted that the number of maximal systems of imprimitivity of a transitive permutation group does not exceed the degree of the group. (Given the conjecture is not quite true, this should be weakened to say that the number of maximal systems of imprimitivity is only a little larger than the degree of the group, and is smaller for many special permutation groups. Such results already exist.

RIP Tim.