Group Theory (LXV): Let G be a group, H a subgroup of G, T an automorphism of G. Let (H)T = {hT| hєH}.Prove (H)T is a subgroup of G.

Modern Algebra Group Theory (LXV) Automorphism of a Group Let G be a group, H a subgroup of G, T an automorphism of G. Let (H)T = {hT| hєH} Prove (H)T is a subgroup of G.

Group Theory (LXVI): Let G be a group, T an automorphism of G, N a normal subgroup of G. Prove that (N)T is a normal subgroup of G.

Modern Algebra Group Theory (LXVI) Automorphism of a Group Let G be a group, T an automorphism of G, N a normal subgroup of G. Prove that (N)T is a normal subgroup of G.

Group Theory (LXVII): Prove that I(G), the set of all inner automorphisms of G is a subgroup of Aut(G), the set all automorphisms of G.

Modern Algebra Group Theory (LXVII) The Set of all Automorphisms of a Group The Set of all Inner Automorphisms of a Group Prove that I(G), the set of all inner automorphisms of G is a subgroup of Aut(G), the set all automorphisms of G.

Group Theory (LXVIII): Prove that I(G), the set of all inner automorphisms of G is a group.

Modern Algebra Group Theory (LXVIII) The Set of all Inner Automorphisms of a Group Prove that I(G), the set of all inner automorphisms of G is a group.

Group Theory (LXIX): Prove that I(G), the set of all inner automorphisms of G is normal in Aut(G), the set of all automorphisms of G.

Modern Algebra Group Theory (LXIX) The Set of all Automorphisms of a Group The Set of all Inner Automorphisms of a Group Prove that I(G), the set of all inner automorphisms of G is normal in Aut(G), the set of all automorphisms of G.