determined by the element aG. The element a is called the representative element of the left coset aH.
Right Coset : Let (H, ) be a subgroup of (G, ). For any a G, the set of Ha defined by
Ha h * a | h H
is called the right coset of H in G determined by the element aG. The element a is called the representative element of the right coset Ha.
Theorem : Let (H, ) be a subgroup of (G, ). The set of left cosets of H in G form a partition of G. Every element of G belongs to one and only one left coset of H in G.
Do'stlaringiz bilan baham: |