Mennicke symbol

In mathematics, a Mennicke symbol is a map from pairs of elements of a number field to an abelian group satisfying some identities found by . They were named by , who used them in their solution of the congruence subgroup problem.
Definition.
Suppose that "A" is a Dedekind domain and "q" is a non-zero ideal of "A". The set "W""q" is defined to be the set of pairs ("a", "b") with "a" = 1 mod "q", "b" = 0 mod "q", such that "a" and "b" generate the unit ideal.
A Mennicke symbol on "W""q" with values in a group "C" is a function ("a", "b") → [] from "W""q" to "C" such that 
There is a universal Mennicke symbol with values in a group "C""q" such that any Mennicke symbol with values in "C" can be obtained by composing the universal Mennicke symbol with a unique homomorphism from "C""q" to "C".