Publisher's Synopsis
Factorizations of finite groups as a product of two proper subgroups arise naturally in several areas of group theory, geometry, and applications. In this book, the authors determine all factorizations of the finite simple groups and their automorphism groups as a product of two maximal subgroups. The proof involved detailed study of the geometry of simple groups, and there is a substantial introductory section presenting this material.;One of the major unsolved problems in the theory of finite groups is the classification of the maximal subgroups of the finite simple groups and their automorphism groups. As an application of their main results, the authors present an effective classification of the maximal subgroups of one such class, the finite alternating and symmetric groups. Requiring a basic knowledge of group theory, the book is directed at research mathematicians and graduate students.
