ABSTRACT RADICES

Radices arose naturally in previous efforts to classify normal subgrou ps of SL(2, A) and Sp(4, A), A a commutative ring. They appeared as su bstructures of A and the matrix algebra M-2(A), respectively, associat ed with normal subgroups, and defined by some seemingly ad hoc closure properties. In this paper we give an abstract, axiomatic definition o f radices, which should be the correct definition in any context to wh ich the axioms apply.