ABSTRACT
This chapter examines a different but related internal structure created by what are called cosets. In this case, we fix a given subgroup H of a given group G and form its cosets (denoted H, a * H, b * H, etc.) which have the following three properties: every coset has the same cardinality as H; every coset has empty intersection with all the other cosets; and the union of all the cosets is the entire group G. The cosets of H in G are said then to partition G into sets all of the same cardinality. This is very powerful internal structure, and it exists in every group, finite or infinite, Abelian or non-Abelian.
