Let
G be a finite group and H a subgroup of G. Let a be an...
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LetG be a finite group and H a subgroup of G. Let a be an element of Gand aH = {ah : h is an element of H} be a left coset of H. If b isan element of G as well and the intersection of aH bH is non-emptythen aH and bH contain the same number of elements in G. Thusconclude that the number of elements in H, o(H), divides the numberof elements in G, o(G).
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