Standard subgroups of GL2(A)

Abstract

Let R be a commutative ring and let q be an ideal in R. Let En(R) be the subgroup of GLn(R) generated by the elementary matrices and let En(q) be the normal subgroup of En(R) generated by the q-elenientary matrices. The order of a subgroup S of GLn(R) is the ideal q0 in R generated by xij, xii−xjj, where (xij)∈S, with 1≦i, j≦n and i≠j. The subgroup S is called a standard subgroup if En(q0)≦S. An almost-normal subgroup of GLn(R) is a non-normal subgroup which is normalized by En(R).