Let G be any group and A (G) the set of all 1-1 mappings of G, as a set, onto itself. Define La: G→ G by La(x) = xa¹. Prove that: (a) La E A (G). (b) LaLb= Lab. (c) The mapping : GA (G) defined by (a) = La is a monomor- phism of G into A (G).

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