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^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, C₁ over G₁ and C₂ over G₂, are defined to be conformant if there exists a bijective mapping between the group codes, ψ_∞:C₁→C₂, such that it is the component-wise application of a group bijection ψ:G₁ →G₂ (and with ψ(1)=l)