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Suppose G {\displaystyle G} is a group, H {\displaystyle H} is a subgroup and α {\displaystyle \alpha } is an endomorphism of G {\displaystyle G} with the property that α ( g ) ∈ H {\displaystyle \alpha (g)\in H} for all g ∈ H {\displaystyle g\in H} . Then, the restriction of α {\displaystyle \alpha } to H {\displaystyle H} defines an endomorphism of H {\displaystyle H} .
