Wikipedia:Reference desk/Archives/Mathematics/2013 June 22

= 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)
 * 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.