Centre of a group: Difference between revisions

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The centre is a [[subgroup]], which is [[normal subgroup|normal]] and indeed [[characteristic subgroup|characteristic]].  It may be described as the set of elements by which [[conjugation (group theory)|conjugation]] is trivial (the identity map); this shows the centre as the [[kernel of a homomorphism|kernel]] of the [[group homomorphism|homomorphism]] to ''G'' to its [[inner automorphism]] group.
The centre is a [[subgroup]], which is [[normal subgroup|normal]] and indeed [[characteristic subgroup|characteristic]].  It may be described as the set of elements by which [[conjugation (group theory)|conjugation]] is trivial (the identity map); this shows the centre as the [[kernel of a homomorphism|kernel]] of the [[group homomorphism|homomorphism]] to ''G'' to its [[inner automorphism]] group.
==See also==
* [[Centraliser]]
* [[Centre (mathematics)]]


==References==
==References==
* {{cite book | author=Marshall Hall jr | title=The theory of groups | publisher=Macmillan | location=New York | year=1959 | pages=14 }}
* {{cite book | author=Marshall Hall jr | title=The theory of groups | publisher=Macmillan | location=New York | year=1959 | pages=14 }}

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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,

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.

References

  • Marshall Hall jr (1959). The theory of groups. New York: Macmillan, 14.