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For fixed g ∈ g g ∈ g, prove that conjugation by g g is an isomorphism from g g onto itself (i. e. An automorphism of g g). Deduce that x x and gxg−1 g x g 1 have that same order for all x ∈ g x ∈ g.
For fixed g ∈ g g ∈ g, prove that conjugation by g g is an isomorphism from g g onto itself (i. e. An automorphism of g g). Deduce that x x and gxg−1 g x g 1 have that same order for all x ∈ g x ∈ g.