Groups with commutator relations

Abstract

The chapter begins with two sections developing some of the combinatorics required for the rest. Instead of restricting ourselves to root systems in the usual sense and with a view towards later applications, we base at least part of the theory on “sets in free abelian groups”, that is, pairs (R, X) consisting of a free abelian group X and a subset R of X generating X and containing 0. With an obvious definition of morphisms, they form a category SF.