Centre of a group: Difference between revisions

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In group theory, the centre of a group is the subset of elements which commute with every element of the group.

Formally,

Z(G)=\{z\in G:\forall x\in G,~xz=zx\}.\,

The centre is a subgroup, which is normal and indeed characteristic. It may be described as the set of elements by which conjugation is trivial (the identity map); this shows the centre as the kernel of the homomorphism to G to its inner automorphism group.

Revision as of 14:29, 15 November 2008 (view source) imported>Richard Pinch (def in terms of trivial conjugation) ← Older edit		Revision as of 11:27, 13 February 2009 (view source) imported>Chris Day No edit summary Newer edit →
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	In [[group theory]], the '''centre of a group''' is the subset of elements which [[commutativity\|commute]] with every element of the group.		In [[group theory]], the '''centre of a group''' is the subset of elements which [[commutativity\|commute]] with every element of the group.