we know that all sylow 3-subgroups are conjugate to each other. if every element in h1 commutes with y, then conjugation by elements of h1 will not change y, and it would not be able to map k1 to another sylow 3-subgroup. this contradicts the sylow theorems, which state that all sylow 3-subgroups are conjugate. therefore, there must be some non-identity element in h1, say v, such that vyv^(-1)