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Defined cosets for subgroups:
  Let H be a subgroup of a group G. aH = {ah | h in H} is the left
  coset of H containing a, while Ha = {ha | h in H} is the right
  coset of H containing a.

The cosets of H are subsets of G.

Suppose f: G1 -> G2 is a group homomorphism of G1 into G2; H is the
kernel of f. For any a in G1, aH = Ha = { x in G1 | f(x) = f(a) }.
(This is proved in Czf_itt_hom.)

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