  This paper presents a classification of exact factorizations of almost simple
groups, which have been a long-standing open problem initiated by the work of
Wiegold and Williamson in 1980 and significantly progressed by Liebeck, Praeger
and Saxl in 2010. The classification is then used to confirm a conjecture of
Etingof, Gelaki, Guralnick and Saxl in 2000 on bicrossproduct Hopf algebras.
