1. The problem statement, all variables and given/known data The group [tex]G[/tex] acts transitively from the left on the set [tex]X[/tex]. Let [tex]G_x [/tex] be the little group of the element [tex]x \epsilon X[/tex]. Show that the map [tex]i:G/G_x[/tex], [tex]i(gG_x)=gx[/tex] is well defined and bijective. 2. Relevant equations transitive action:for any two x, y in X there exists a g in G such that g·x = y 3. The attempt at a solution Transitive action shows that [tex]x \epsilon X[/tex], [tex]g \epsilon G[/tex] [tex]->[/tex] [tex]g·x \epsilon X[/tex]. This shows that the mapping is a surjection. Now how do i show that it's an injection? And obviously the bijection thing shows that the function is well defined, right? Even the injection would suffice for this?