Prove Theorem 10.14 [Hint: Let {ai H ǀ i = 1. •••, r} be the collection of distinct left cosets of H in G and {bjK ǀ j = 1, •••, s] be the collection of distinct left cosets of K in H. Show that {(aibj)K ǀ i = 1. •••. r; j = 1. •••..s} is the collection of distinct left cosets of K in G.]
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