Many non-abelian groups support only group codes that are conformant to abelian group codes

Define a group code C over a group (G,*,1) to be a subgroup of the sequence space G/sup Z/ that is stationary and is not also a subgroup of a sequence space defined on a proper subgroup of G. In addition, consider group codes to be finitely-controllable and complete. This implies that there exist minimal sets of finite-length encoder sequences that will causally encode the group code like an impulse response system over the group G. A non-abelian group code is a group code over a non-abelian group. Two group codes, C/sub 1/ over G/sub 1/ and C/sub 2/ over G/sub 2/, are defined to be conformant if there exists a bijective mapping between the group codes, /spl psi//sub /spl infin//:C/sub 1//spl rarr/C/sub 2/, such that it is the component-wise application of a group bijection /spl psi/:G/sub 1//spl rarr/G/sub 2/ (and with /spl psi/(1)=l).