Differential coding: Difference between revisions

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In [[mathematics]], in the field of [[group theory]], a [[subgroup]] of a [[group (mathematics)|group]] is termed '''central''' if it lies inside the center of the group.
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Given a group <math>G</math>, the [[center (group theory)|center]] of <math>G</math>, denoted as <math>Z(G)</math>, is defined as the set of those elements of the group which commute with every element of the group. The center is a [[characteristic subgroup]] and is also an [[abelian group]] (because, in particular, all elements of the center must commute with each other). A subgroup <math>H</math> of <math>G</math> is termed ''central'' if <math>H \leq Z(G)</math>.
 
Central subgroups have the following properties:
 
* They are abelian groups.
* They are [[normal subgroup]]s. In fact, they are [[central factor]]s, and are hence [[transitively normal subgroup]]s.
 
== References ==
* {{springer|id=C/c021250|title=Centre of a group}}.
 
[[Category:Subgroup properties]]

Latest revision as of 04:46, 13 May 2014

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