we are given H is a subgroup of G and whenever have Ha not equal to Hb...then aH is not equal to bH.....we have to prove that g.H.(g^-1) is a subset of H...thnx in advance...
we are given H is a subgroup of G and whenever have Ha not equal to Hb...then aH is not equal to bH.....we have to prove that g.H.(g^-1) is a subset of H...thnx in advance...
Firstly, you should prove that left and right cosets coincide precisely (you will need to use your assumption to prove this). That is, for all there exists an such that . How does this help you? (You will need a second application of your assumption here.)