The Number of Generators of a Finite Group

Abstract

In this expository article, which is a slightly expanded version of the lecture given at the All Ireland Algebra Days (Belfast, 16-19 May, 2001), we first recall a technique recently developed by F. Dalla Volta and A. Lucchini to study generation properties of finite groups. We then discuss some problems in permutation groups, linear groups and profinite groups where this technique has proved useful. Finally, we comment on some results and problems related to probability and computation.