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Definition of a subgroup h

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Reference no: EM131985701

Recall that the center of a group G is Z(G)={x∈G:xg=gx,∀g∈G}. That is, the set of all elements which commute with every element of G. Use the following definition of a subgroup H being a normal subgroup to show that Z(G)is a normal subgroup of G:A subgroup H of G is a normal subgroup of G if for all g∈G we have g^(-1) Hg=H.

Reference no: EM131985701

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