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Mathematics, 26.11.2019 23:31 vince022503
Let h be a subgroup of a group g. we call h characteristic in g if for any automorphism σ∈aut(g) of g, we have σ(h)=h.
(a) prove that if σ(h)⊂h for all σ∈aut(g), then h is characteristic in g.
(b) prove that the center z(g) of g is characteristic in g.
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