Center (group theory)

Cayley table of Dih4, the dihedral group of order 8.The center is 0,7: The row starting with 7 is the transpose of the column starting with 7. The entries 7 are symmetric to the main diagonal. (Only for the neutral element this is granted in all groups.)

In abstract algebra, the center of a group G, denoted Z(G), is the set of elements that commute with every element of G. In set-builder notation,

The center is a subgroup of G, which by definition is abelian (that is, commutative). As a subgroup, it is always normal, and indeed characteristic, but it need not be fully characteristic. The quotient group G / Z(G) is isomorphic to the group of inner automorphisms of G.

单词	Centerless
释义	Centerless 英语百科 Center (group theory) In abstract algebra, the center of a group G, denoted Z(G), is the set of elements that commute with every element of G. In set-builder notation, The center is a subgroup of G, which by definition is abelian (that is, commutative). As a subgroup, it is always normal, and indeed characteristic, but it need not be fully characteristic. The quotient group G / Z(G) is isomorphic to the group of inner automorphisms of G.
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Centerless

Center (group theory)