Let G be anon-commutative group. Consider all the one-to-one mappings a→a′ of G onto itself such that (ab)'\equal{}b'a' (i.e. the anti-automorphisms of G). Prove that this mappings together with the automorphisms of G constitute a group which contains the group of the automorphisms of G as direct factor. group theorysuperior algebrasuperior algebra unsolved