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.
Suppose that A is a Dedekind domain and q is a non-zero ideal of A. The set W<sub>q</sub> 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<sub>q</sub> with values in a group C is a function (a, b) â [] from W<sub>q</sub> to C such that
There is a universal Mennicke symbol with values in a group C<sub>q</sub> such that any Mennicke symbol with values in C can be obtained by composing the universal Mennicke symbol with a unique homomorphism from C<sub>q</sub> to C.