Note: I only need help on the underlined portion of the problem, but I'm including all parts since they may provide relevant information. Thanks in advance. 1. The problem statement, all variables and given/known data Let S be a subset of a group G such that g−1Sg ⊂ S for any g∈G. Show that the subgroup ⟨S⟩ generated by S is normal. Let T be any subset of G and let S = g−1Tg. Show that ⟨S⟩ is the normal subgroup generated by T. 3. The attempt at a solution I apply the first part of the problem to see that <S> is normal, and that is as far as I am getting. I know that <S> ⊇ <T> by the definitions, but since we have such little information about T I can't get much further. If the normal/"ordinary" subgroups containing S and T were the same then the conclusion would be obvious but the definition of G seems to preclude this.