Hello, I am having trouble with the following problem. Suppose that H is a subgroup of G such that whenever Ha≠Hb then aH≠bH. Prove that gHg^(-1) is a subset of H. I have tried to manipulate the following equation for some ideas H = Hgg^(-1) = gg^(-1)H but I don't know how to go from here. I can't figure out how I can use the conditions to show that every element in gHg^(-1) is also in H. I also know that gHg^(-1) is a subgroup of G, but I don't know if this fact can be used here. It well be great if someone can point me in the right direction. Thank you.