Factorizations of Finite Groups and Related Topics

Abstract

This is a survey on the recent progress in the theory of finite groups with factorizations and around it, done by the author and his co-authors, and this has no pretensions to cover all topics in this wide area of research. In particular, we only touch the great consequences of the fundamental paper of Liebeck, Praeger and Saxl on maximal factorizations of almost simple finite groups for the theory of groups with factorizations. In each case the reader can find additional references at the end of Section 1. Some of the methods of investigation can be used to obtain information about finite groups in general, nilpotent algebras and related nearrings.