Elements of a color group C are colored in the following way. The
elements having the same color as
C.identity form a subgroup H, which
has finite index n in C. H is called the
ColorSubgroup of C.
Elements of C have the same color if and only if they are in the same
right coset of H in C. A fixed list of right cosets of H in C,
ColorCosets, therefore determines a labelling of the colors,
which runs from 1 to n. Elements of H by definition have color 1,
i.e., the coset with representative
C.identity is always the first
ColorCosets. Right multiplication by a fixed element g of
C induces a permutation p(g) of the colors of the parent of C.
This defines a natural homomorphism of C into the permutation group of
degree n. The image of this homomorphism is called the
ColorPermGroup of C, and the homomorphism to it is called the
ColorHomomorphism of C.
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