Electromagnetic tensor - Revision history

en>Quince Pan at 04:51, 20 December 2014

2014-12-20T04:51:14Z

← Older revision		Revision as of 06:51, 20 December 2014
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en>JohnBlackburne: Reverted 1 edit by 109.145.241.109 (talk): Article's not broken, and WP is now fixed. (TW)

2014-02-08T21:59:53Z

Reverted 1 edit by 109.145.241.109 (talk): Article's not broken, and WP is now fixed. (TW)

← Older revision		Revision as of 23:59, 8 February 2014
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	~~{{For\|the counting result sometimes called "Burnside's theorem"\|Burnside's lemma}}~~
	~~In [[mathematics]], '''Burnside's theorem''' in [[group theory]] states that if ''G'' is a [[finite group]] of [[Order (group theory)\|order]]~~

	~~:<math>p^a q^b\ </math>~~

	~~where ''p''~~ and '~~'q'' are [[prime number]]s, and ''~~a'' and ~~''b''~~ are [~~[negative and positive numbers\|non-negative]] [[integer]]s, then ''G'' is [[Solvable group\|solvable]]~~. ~~Hence each~~		The other day I woke up and realised - At the moment I've been single for a while and after much intimidation from buddies I now locate myself signed up for web dating. They promised me that there are a lot [http://www.netpaw.org luke bryan concert tickets 2014] of sweet, normal and fun folks to meet, therefore the pitch is gone by here!<br>I endeavor to keep as physically healthy as possible staying at the [http://search.Un.org/search?ie=utf8&site=un_org&output=xml_no_dtd&client=UN_Website_en&num=10&lr=lang_en&proxystylesheet=UN_Website_en&oe=utf8&q=gymnasium+several-times&Submit=Go gymnasium several-times] per week. I appreciate my sports and attempt to perform or view as many a potential. I [http://okkyunglee.com luke Bryan 2014 tour dates] will often at Hawthorn fits being wintertime. Note: In case [http://www.ladyhawkshockey.org find luke bryan Tickets] that you really considered purchasing an activity I don't brain, I've observed the carnage of wrestling matches at stocktake revenue.<br>My friends and fam are wonderful and spending time with them at bar gigs or meals is constantly vital. I have never been in to nightclubs as I locate that you can not own a significant conversation against the sound. Additionally, I have 2 undoubtedly cheeky and really cunning canines who are invariably eager to meet up fresh individuals.<br><br>Here is my blog [http://lukebryantickets.hamedanshahr.com luke bryan t]
	~~non-Abelian [[finite simple group]] has order divisible by at least three distinct primes~~.

	~~==History==~~
	~~The theorem was proved by [[William Burnside]~~] ~~in the early years~~ of ~~the 20th century.~~

	~~Burnside's theorem has long been one of the best-known applications of [[Representation theory of finite groups\|representation theory]]~~ to ~~the theory of finite groups~~, ~~though a proof avoiding~~ the ~~use of group characters was published~~ by D. ~~Goldschmidt around 1970~~.

	==~~Outline of Burnside's proof~~==
	# By induction, it suffices to prove that a finite simple group ''G'' whose order has the form <math>p^a q^b </math> for primes ''p'' and ''q'' is cyclic. Suppose then that the order of ''G'' has this form, but ''G'' is not cyclic. Suppose for definiteness that ''b''&~~nbsp;>~~&~~nbsp;0.~~
	~~# Using the modified class equation, ''G'' has a non~~-~~identity conjugacy class of size prime to ''q''. Hence ''G'' either has a non~~-~~trivial [[Group center\|center~~]], or ~~has~~ a [~~[conjugacy class]] of size <math>p^r<~~/math> for some positive integer ''r''. The first possibility is excluded since ''G'' is assumed simple, but not cyclic. Hence there is a non-central element ''x'' of ''G'' such that the conjugacy class of ''x'' has size <math>p^r</~~math>~~.
	~~# Application of [[Character theory\|column orthogonality relations~~]~~] and other properties of group characters and algebraic integers lead to the existence of a non-trivial~~ [~~[Character theory\|irreducible character]] <math>\chi<~~/~~math> of ''G'' such that <math>\|\chi(x)\| = \chi(1)<~~/~~math>~~.
	~~# The simplicity of ''G'~~' ~~then implies that any non-trivial complex irreducible representation is faithful~~, ~~and it follows that ''x'~~' ~~is in~~ the ~~center~~ of ~~''G'', a contradiction~~.

	~~==References==~~
	~~# James, Gordon;~~ and ~~Liebeck, Martin (2001). ''Representations~~ and ~~Characters of Groups'' (2nd ed~~.). ~~Cambridge University Press. ISBN 0-521-00392-X. See chapter 31.~~
	~~# Fraleigh~~, ~~John B~~. ~~(2002) ''A First Course in Abstract Algebra'' (7th ed.). Addison Wesley~~. ~~ISBN 0-201-33596-4~~.

	~~[[Category:Theorems in group theory]~~]

en>Airwoz: /* Lagrangian formulation of classical electromagnetism (no charges and currents) */

2014-01-07T20:16:47Z

Lagrangian formulation of classical electromagnetism (no charges and currents)

← Older revision		Revision as of 22:16, 7 January 2014
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	[~~http://warrenmooretgqn.newsvine.com/_news/2014/08/07/25216527-the-dos-and-donts-of-her-kan-du-ogs-spille-p-norske-spilleautomater-helt erfaring spilleautomater~~] ~~Friends contact her Sharilyn but people always misspell it.~~ [~~http://www.purevolume.com/sonjamacnaghten/posts/6917247/Here%92s+A+Quick+Way+To+Solve+The+Her+Kan+Du+Pr%C3%B8ve+Deg+P%C3%A5+Spilleautomater+P%C3%A5+Nettet+Problem norske spilleautomater på nett~~] ~~Curing people~~ is ~~how I make cash but soon my husband and I will begin our~~ [~~http://www.purevolume.com/sonjamacnaghten/posts/6928024/Six+Very+Simple+Things+You+Can+Do+To+Save+Norskeautomater gjennomgang gällande european gambling establishment my partner and i norge~~] ~~personal company. To act is what adore doing. District~~ of [http://Www.Bing.com/search?q=Columbia&form=MSNNWS&mkt=en-us&pq=Columbia Columbia] is where [https://www.rebelmouse.com/shermanwalls/having-a-provocative-norskeaut-650378554.html spilleautomater] I've usually [~~http://www.purevolume.com/murrayrossetti/posts/6894253/A+Guide+To+Ta+En+Titt+P%C3%A5+Min+Liste+Over+Norske+Spilleautomater spilleautomater norske~~] ~~been [https://www.rebelmouse.com/shermanyfgwlxqitt/the-spilleautomat-trap-660856703.html gjennomgang villig western european internet casino i norge~~] ~~residing. Check out her website here: http://www.purevolume.com/melodymabrydn/posts/6900635/What+Everyone+Ought+To+Know+About+Beste+Automater+P%C3%A5+Nett<br><br>~~		{{For\|the counting result sometimes called "Burnside's theorem"\|Burnside's lemma}}
			In [[mathematics]], '''Burnside's theorem''' in [[group theory]] states that if ''G'' is a [[finite group]] of [[Order (group theory)\|order]]

	~~my page :~~: [~~http:~~//~~www~~.~~purevolume~~.~~com~~/~~melodymabrydn~~/~~posts~~/~~6900635/What+Everyone+Ought+To+Know+About+Beste+Automater+P%C3%A5+Nett spilleautomat kungen nett~~]		:<math>p^a q^b\ </math>

			where ''p'' and ''q'' are [[prime number]]s, and ''a'' and ''b'' are [[negative and positive numbers\|non-negative]] [[integer]]s, then ''G'' is [[Solvable group\|solvable]]. Hence each
			non-Abelian [[finite simple group]] has order divisible by at least three distinct primes.

			==History==
			The theorem was proved by [[William Burnside]] in the early years of the 20th century.

			Burnside's theorem has long been one of the best-known applications of [[Representation theory of finite groups\|representation theory]] to the theory of finite groups, though a proof avoiding the use of group characters was published by D. Goldschmidt around 1970.

			==Outline of Burnside's proof==
			# By induction, it suffices to prove that a finite simple group ''G'' whose order has the form <math>p^a q^b </math> for primes ''p'' and ''q'' is cyclic. Suppose then that the order of ''G'' has this form, but ''G'' is not cyclic. Suppose for definiteness that ''b'' > 0.
			# Using the modified class equation, ''G'' has a non-identity conjugacy class of size prime to ''q''. Hence ''G'' either has a non-trivial [[Group center\|center]], or has a [[conjugacy class]] of size <math>p^r</math> for some positive integer ''r''. The first possibility is excluded since ''G'' is assumed simple, but not cyclic. Hence there is a non-central element ''x'' of ''G'' such that the conjugacy class of ''x'' has size <math>p^r</math>.
			# Application of [[Character theory\|column orthogonality relations]] and other properties of group characters and algebraic integers lead to the existence of a non-trivial [[Character theory\|irreducible character]] <math>\chi</math> of ''G'' such that <math>\|\chi(x)\| = \chi(1)</math>.
			# The simplicity of ''G'' then implies that any non-trivial complex irreducible representation is faithful, and it follows that ''x'' is in the center of ''G'', a contradiction.

			==References==
			# James, Gordon; and Liebeck, Martin (2001). ''Representations and Characters of Groups'' (2nd ed.). Cambridge University Press. ISBN 0-521-00392-X. See chapter 31.
			# Fraleigh, John B. (2002) ''A First Course in Abstract Algebra'' (7th ed.). Addison Wesley. ISBN 0-201-33596-4.

			[[Category:Theorems in group theory]]

en>Teply: /* See also */ RS vector is pretty much the same thing, just recast in GA

2012-09-02T10:06:54Z

See also: RS vector is pretty much the same thing, just recast in GA

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