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.
随便看	sploofs splooge splooged splooges splooging Sploosh splooshed splooshes splop splore Splork splorking splosh sploshy SPLOST Splot splotch splotchy splotchiness splots splotty SPLR spl special SPLTARY SPLTY

Centerless

Center (group theory)