en>R'n'B: Fix links to disambiguation page CCS

2013-03-04T17:01:45Z

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	~~Irwin Butts~~ is ~~what my wife enjoys~~ to ~~contact me though I don~~'~~t really like being known as like that~~. ~~Body developing~~ is ~~what my family and I enjoy. He used~~ to ~~be unemployed but now he~~ is a ~~meter reader. My family lives~~ in ~~Minnesota and my family enjoys it.~~<br><br>~~Here~~ is ~~my website [http:~~//~~www~~.~~animecontent~~.~~com/blog/436250 www~~.~~animecontent~~.~~com~~]		{{Orphan\|date=February 2013}}

			In [[mathematics]], in the field of [[group theory]], a [[subgroup]] of a [[group (mathematics)\|group]] is said to be '''fully normalized''' if every automorphism of the subgroup lifts to an [[inner automorphism]] of the whole group. Another way of putting this is that the natural embedding from the [[Weyl group]] of the subgroup to its [[automorphism group]] is surjective.

			In symbols, a subgroup <math>H</math> is fully normalized in <math>G</math> if, given an automorphism <math>\sigma</math> of <math>H</math>, there is a <math>g \in G</math> such that the map <math>x \mapsto gxg^{-1}</math>, when restricted to <math>H</math> is equal to <math>\sigma</math>.

			Some facts:
			* Every group can be embedded as a [[normal subgroup\|normal]] and fully normalized subgroup of a bigger group. A natural construction for this is the [[holomorph (mathematics)\|holomorph]], which is its [[semidirect product]] with its automorphism group.
			* A [[complete group]] is fully normalized in any bigger group in which it is embedded because every automorphism of it is inner.
			* Every fully normalized subgroup has the [[automorphism extension property]].

			{{Unreferenced\|date=April 2009}}

			[[Category:Group theory]]
			[[Category:Subgroup properties]]


			{{Abstract-algebra-stub}}

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2009-02-20T13:32:23Z

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Irwin Butts is what my wife enjoys to contact me though I don't really like being known as like that. Body developing is what my family and I enjoy. He used to be unemployed but now he is a meter reader. My family lives in Minnesota and my family enjoys it.<br><br>Here is my website [http://www.animecontent.com/blog/436250 www.animecontent.com]

Temporal Process Language - Revision history

en>R'n'B: Fix links to disambiguation page CCS

en>Addbot: Bot: Adding Orphan Tag (Questions) (Report Errors)