# (solution) * Let G be a permutation group on a finite number of symbols. Show that if two subgroups H 1 and H 2

* Let G be a permutation group on a finite number of symbols. Show that if two subgroups H 1 and H 2 are conjugate in G , then the permutations in H 2 may be obtained from those in H 1 by renaming the symbols in the permutations. For example, {() , (12)} and {() , (23)} are conjugate in S 3 , and one subgroup can be obtained from the other by renaming 1 i→ 2, 2 i→ 3, and 3 i→ 1.