Relational operator - Revision history

77.56.53.183: /* Confusion with assignment operators */

2015-01-01T23:34:07Z

Confusion with assignment operators

en>Omnipaedista: per MOS:CAPS

2014-02-27T09:19:14Z

← Older revision		Revision as of 11:19, 27 February 2014
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	~~In [[mathematics]]~~, ~~especially in the area of [[abstract algebra\|algebra]] known as [[group theory]], the '''Prüfer rank''~~' of ~~a [[pro-p group]] measures~~ the ~~size of a group~~ in ~~terms of~~ the ~~ranks of its [[elementary abelian group\|elementary abelian]] [[section (group theory)\|section]]s. The rank~~ is ~~well behaved and helps~~ to ~~define analytic pro-p-groups~~. ~~The term is named after [[Heinz Prüfer]]~~.		Nice to satisfy you, my title is Figures Held though I don't really like becoming called like that. My working day job is a meter reader. One of the very best things in the world for him is to collect badges but he is having difficulties to find time for it. Years in the past he moved to North Dakota and his family enjoys it.<br><br>Stop by my blog :: [http://P80.co/diettogo30380 healthy food delivery]

	~~== Definition ==~~

	~~The Prüfer rank of [[pro-p-group]]~~ <~~math~~>G<~~/math~~> is

	::~~<math>\sup\{d(H)\|H\leq G\}</math>~~

	~~where <math>d(H)</math> is the~~ [~~[rank of an abelian group\|rank]] of the abelian group~~

	:~~<math>H~~/~~\Phi(H)<~~/~~math>,~~

	~~where <math>\Phi(H)</math> is the [[Frattini subgroup]] of <math>H</math>~~.

	~~As the Frattini subgroup of <math>H</math> can be thought of as the group of non-generating elements of <math>H</math>, it can be seen that <math>d(H)<~~/~~math> will be equal to the ''size of any minimal generating set'' of <math>H</math>.~~

	~~== Properties ==~~
	~~Those [[profinite group]]s with finite Prüfer rank are more amenable to analysis.~~

	Specifically in the case of finitely generated [[pro-p group]]s, having finite Prüfer rank is equivalent to having an [[open set\|open]] [[normal subgroup]] that is [[powerful p-groups\|powerful]]. In turn these are precisely the class of [[pro-p group]]s that are [[p-adic number\|p-adic]] analytic - that is groups that can be imbued with a
	~~[[p-adic number\|p-adic]] [[manifold]] structure.~~

	~~== References ==~~
	~~{{unref\|date=March 2008}}~~

	~~{{DEFAULTSORT:Prufer Rank}}~~
	~~[[Category:Infinite group theory]~~]

en>Derek farn: Undid revision 582042068 by 125.60.156.207 (talk)

2013-11-17T13:46:40Z

Undid revision 582042068 by 125.60.156.207 (talk)

← Older revision		Revision as of 15:46, 17 November 2013
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	~~Luke is actually~~ a ~~superstar within~~ the ~~producing along with~~ the ~~profession development initial next to his 3rd theatre recording,~~ ~~& ,~~ is ~~the confirmation. He broken~~ to ~~the picture in 2000 regarding his amusing mix of downward~~-~~residence availability, video celebrity fantastic looks and~~ ~~lyrics,~~ is ~~defined t inside a luke bryan in concert (~~[~~http://lukebryantickets.iczmpbangladesh.org lukebryantickets.iczmpbangladesh.org~~]~~) main way~~. The ~~brand new recor on the nation graph or chart and #2 on the pop graphs, building it the second top very first during those times~~ of ~~2000 for the nation performer.~~ <br><br>~~The son of any [http~~://~~lukebryantickets.flicense.com justin bieber concerts~~] ~~, understands patience and willpower are key elements in terms~~ of ~~an effective occupation- . His initial album, Stay Me, made~~ the ~~Top reaches “All My Buddies “Country and Say” Man,” when his effort~~, ~~Doin’ Issue, identified the performer-3 directly No. 9 single men and women: In addition Calling Can be a Very good Point.”~~<br><br>~~While in~~ [~~http:~~//~~lukebryantickets.neodga.com sell tickets]~~ the ~~slip~~ of ~~2000, Concert tour: Luke & which in fact had a remarkable selection~~ of , ~~which includes Urban. “It’s much like you’re acquiring a authorization to go to another level, luke bryan concert tour dates~~ (~~[http:~~//~~lukebryantickets~~.~~lazintechnologies~~.~~com related website~~]~~) affirms these designers which were~~ an ~~element of the Concert tourmore than into a larger degree of musicians~~.~~” It packaged among the best~~ ~~trips in~~ the ~~ten~~-~~season background~~.~~<br><br>Feel free to visit my site;~~ [~~http~~:~~//www.banburycrossonline.com luke bryan in concert~~]		In [[mathematics]], especially in the area of [[abstract algebra\|algebra]] known as [[group theory]], the '''Prüfer rank''' of a [[pro-p group]] measures the size of a group in terms of the ranks of its [[elementary abelian group\|elementary abelian]] [[section (group theory)\|section]]s. The rank is well behaved and helps to define analytic pro-p-groups. The term is named after [[Heinz Prüfer]].

			== Definition ==

			The Prüfer rank of [[pro-p-group]] <math>G</math> is

			::<math>\sup\{d(H)\|H\leq G\}</math>

			where <math>d(H)</math> is the [[rank of an abelian group\|rank]] of the abelian group

			:<math>H/\Phi(H)</math>,

			where <math>\Phi(H)</math> is the [[Frattini subgroup]] of <math>H</math>.

			As the Frattini subgroup of <math>H</math> can be thought of as the group of non-generating elements of <math>H</math>, it can be seen that <math>d(H)</math> will be equal to the ''size of any minimal generating set'' of <math>H</math>.

			== Properties ==
			Those [[profinite group]]s with finite Prüfer rank are more amenable to analysis.

			Specifically in the case of finitely generated [[pro-p group]]s, having finite Prüfer rank is equivalent to having an [[open set\|open]] [[normal subgroup]] that is [[powerful p-groups\|powerful]]. In turn these are precisely the class of [[pro-p group]]s that are [[p-adic number\|p-adic]] analytic - that is groups that can be imbued with a
			[[p-adic number\|p-adic]] [[manifold]] structure.

			== References ==
			{{unref\|date=March 2008}}

			{{DEFAULTSORT:Prufer Rank}}
			[[Category:Infinite group theory]]

2.228.5.114: /* Object identity vs. Content equality */ '=' vs '==' in ocaml/smalltalk were inversed

2012-05-19T23:32:24Z

Object identity vs. Content equality: '=' vs '==' in ocaml/smalltalk were inversed

New page

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