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Miklos Schweitzer 1952_5

Source:

October 12, 2008
group theorysuperior algebrasuperior algebra unsolved

Problem Statement

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