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Centers and Centralizers

Centers and Centralizers. The Center of a group. Definition: Let G be a group. The center of G, denoted Z(G) is the set of group elements that commutes with every element of G. That is, . Z(D 4 ). Z(D 4 ) contains R 0. Z(D 4 ) contains R 180. Z(D 4 ). = {R 0 , R 180 }. Z(G)?G.

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Centers and Centralizers