Please solve this question

17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. If G is a group, prove that Aut(G) and Inn(G) are groups. (This exercise is referred to in this chapter.) If a group G is isomorphic to H, prove that Aut(G) is isomorphic to Aut(H). Suppose (1'; belongs to Aut(Z) and a is relatively prime to n. If (Ma) 2 1:, determine a formula for (x). Let H be the subgroup of all rotations in D\" and let qb be an automor- phism of DH. Prove that (H) = H. (In words, an automorphism of DH carries rotations to rotations.) LetH== { E S5 [18(1)= 1}andK= {3 E 35 i(2) = 2}.Prove that H is isomorphic to K. Is the same true if .35 is replaced by S\