An essay on free products of groups with amalgamations

Abstract

Abstract Free products of groups with amalgamated subgroups, first introduced by Schreier (1927) and generalized by Hanna Neumann (1948), are here redefined, studied and applied to a number of problems in abstract group theory. The applications are mainly concerned with existence and embedding theorems. The first four chapters are self-contained, requiring little beyond the fundamentals of abstract group theory. Only in the last chapter is use made of theorems (Gruschko 1940; Kurosch 1934; Hanna Neumann 1949) which are not proved here.