ABSTRACT
This chapter contains the definitions and basic facts on rank, coefficient groups (our replacement for height sequence and characteristic), purity, types of elements, type subgroups, and completely decomposable groups as well as some classical and indispensable tools such as the Baer Lemma. A detailed study of completely de composable groups follows afterwards. In particular, for later use, we need results on lifting of endomorphisms and automorphisms of A jeA to A for completely de composable groups A. There is no restriction on rank in this chapter unless stated otherwise.
