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June 22

double coset question

Given a group G and a subgroup H , and a mapping from G/H into H/G\H defined by f(aH) = HaH for all a in G, f is a bijection if and only if H is normal in G. Remag12 (talk) 22:41, 22 June 2013 (UTC)[reply]

One direction is obvious. For the other show that every left coset is a right coset. Sławomir Biały (talk) 23:54, 22 June 2013 (UTC).It is easier to show if H is not normal in G, then f is not an injection.[reply]