137.138.117.212 at 09:43, 13 November 2013

2013-11-13T09:43:18Z

← Older revision		Revision as of 11:43, 13 November 2013
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	~~Name~~: ~~Winifred Sylvia~~<br>~~Age: 39 years old~~<br>~~Country: Great Britain~~<br>~~City: Exton~~ <br>~~Post code: So32 5hh~~<br>~~Street: 56 Wrexham Rd~~<br><br>~~My webpage~~ - ~~[http:~~//~~www~~.~~douloschurch.com~~/xe/~~index~~.~~php?document_srl~~=~~2640657&mid~~=~~banner анита цой диета~~]		In [[mathematics]], more precisely in [[algebra]], a '''prosolvable group''' (less common: '''prosoluble group''') is a [[group (mathematics)\|group]] that is [[isomorphic]] to the [[inverse limit]] of an [[inverse system]] of [[solvable group]]s. Equivalently, a group is called '''prosolvable''', if, viewed as a [[topological group]], every [[open neighborhood]] of the identity contains a [[normal subgroup]] whose corresponding [[quotient group]] is a [[solvable group]].

			== Examples ==
			* Let ''p'' be a [[prime]], and denote the [[Field (mathematics)\|field]] of [[p-adic numbers]], as usually, by <math>\mathbf{Q}_p</math>. Then the [[Galois group]] <math>\text{Gal}(\overline{\mathbf{Q}}_p/\mathbf{Q}_p)</math>, where <math>\overline{\mathbf{Q}}_p</math> denotes the [[algebraic closure]] of <math>\mathbf{Q}_p</math>, is prosolvable. This follows from the fact that, for any finite [[Galois extension]] <math>L</math> of <math>\mathbf{Q}_p</math>, the [[Galois group]] <math>\text{Gal}(L/\mathbf{Q}_p)</math> can be written as [[semidirect product]] <math>\text{Gal}(L/\mathbf{Q}_p)=(R \rtimes Q) \rtimes P</math>, with <math>P</math> cyclic of order <math>f</math> for some <math>f\in\mathbf{N}</math>, <math>Q</math> cyclic of order dividing <math>p^f-1</math>, and <math>R</math> of <math>p</math>-power order. Therefore, <math>\text{Gal}(L/\mathbf{Q}_p)</math> is [[solvable group\|solvable]].<ref>{{citation\|last=Boston\|first=Nigel\|title=The Proof of Fermat's Last Theorem\|year=2003\|publisher=University of Wisconsin Press\|location=Madison, Wisconsin, USA}}</ref>

			== See also ==
			* [[Solvable group]]
			* [[Galois theory]]
			* [[p-adic integers]]

			==References==
			{{reflist}}

			[[Category:Mathematical structures]]
			[[Category:Algebra]]
			[[Category:Number theory]]
			[[Category:Topology]]
			[[Category:Group theory]]
			[[Category:Topological groups]]

en>ZéroBot: r2.7.1) (Robot: Adding nl:Collineariteitsvergelijking

2012-02-14T23:44:56Z

r2.7.1) (Robot: Adding nl:Collineariteitsvergelijking

New page

Name: Winifred Sylvia Age: 39 years old Country: Great Britain City: Exton Post code: So32 5hh Street: 56 Wrexham Rd My webpage - [http://www.douloschurch.com/xe/index.php?document_srl=2640657&mid=banner анита цой диета]

Collinearity equation - Revision history

137.138.117.212 at 09:43, 13 November 2013

en>ZéroBot: r2.7.1) (Robot: Adding nl:Collineariteitsvergelijking