Review of Subgroup lattices of groups by Roland Schmidt Expositions in Math vol 14 de Gruyter 1994 xv 572 pp 1996

Abstract:  ical considerations to solve the classification problem of finite simple groups." However this hope was not realized; much more powerful techniques, primarily character theory and "local analysis", were used. Similarly in Abelian group theory Baer's lattice theory techniques are no longer used. (See page 86 of Kaplansky's monograph [13].) So group theory and lattice theory went their separate ways. (For that matter, group theory nowadays has little in common with Abelian group theory.) Group theory had other techniques and lattice theory had its own deep problems to work on, and most of the applications of lattice theory to algebra were in the field of universal algebra. In the last several years some connections between lattice theory and group theory have resurfaced. One problem of interest in general algebra: is every finite lattice isomorphic to the congruence lattice of some algebraic system?P.Palfy and 1991 Mathematics Subject Classification. Primary 20E15; Secondary 06B15