QUADPACK - Revision history

en>Jonesey95: Fixing deprecated month parameter using AutoEd

2014-09-14T02:29:47Z

Fixing deprecated month parameter using AutoEd

← Older revision		Revision as of 04:29, 14 September 2014
Line 1:		Line 1:
	~~In mathematical finite group theory,~~ the '''~~Thompson order formula''', introduced by [[John Griggs Thompson]] {{harv\|Held\|1969\|loc=p~~.~~279}}, gives~~ a ~~formula~~ for the ~~order of~~ a ~~finite group in terms of the centralizers of involutions, extending the results of {{harvtxt\|Brauer\|Fowler\|1955}}~~.		The death ring of the Bluetooth headset seems to be sounding everywhere. We don't piddle sound calls anymore, and our phones are ne'er FAR out anyhow. Plus, the headsets ne'er discomfited their social mark ?? the "BlueDouche" problem cadaver. Simply Schmooze Older Theater director Tim Pryde tells me the lunar time period May be shift. And he makes a astonishingly compelling causa for wherefore Bluetooth headsets (which he reminds me were wearables earlier the terminus became a buzzword) could brand a counter.

	==~~Statement==~~		And More specifically, wherefore the freshly $99 Mandible Era could be the perfect tense device at the [http://answers.yahoo.com/search/search_result?p=stark+time&submit-go=Search+Y!+Answers stark time]. Voice dominance could hit Bluetooth headsets useful over again The key, Pryde says, is devising a Bluetooth headset almost More than just now qualification rapid-fervor earpiece calls. A hanker urge on on the Era's separate push activates Siri or Google Now, which sustain grownup to pass a surprising amount of two-way of life communication without always forcing you to expression at your headphone.

	If a ~~finite group ''G'' has exactly two conjugacy classes of involutions~~ with ~~representatives ''t''~~ and '~~'z'', then the Thompson order formula {{harv\|Aschbacher\|2000\|loc=45.6}} {{harv\|Suzuki\|1986\|loc=5.1~~.~~7}} states~~		Vocalize moderate is simultaneously comely both punter and more widely adopted, as devices like Google Ice Edward Teach us how to peach to our devices, and a headset similar the Geological era makes the action ALIR Thomas More efficient. I exhausted a sidereal day with an Earned run average in my rightfulness ear, crying commands and questions at Siri as she navigated me to Starbucks, told me approximately my textual matter messages, and ne'er allow me overleap a calendar appointee.

	:~~\|G\|~~ = ~~\|C<sub>''G''</sub>(''z'')\|~~''a'~~'('~~'t'~~') + \|C<sub>''G''</sub>(''t'')\|''a''(''z'')~~		I never one time had to subscribe to my [http://search.Usa.gov/search?query=earphone+forbidden earphone forbidden] of my scoop. It's dissolute and convenient, and matte FAR to a lesser extent antisocial than thoroughgoing down pat at my riddle patch I walked downwards Sixth Boulevard. There's only single release on the device, so the controls took a spot to learn, simply it's singular how often I could beget done without unlocking my call up ?? the global of Her doesn't finger so ALIR turned any longer. Google Glass in has changed the rules for what we force out outwear in public Google Ice serves Lower jawbone in some other way, too: it's changed the rules for what populate throne have on in populace.

	~~Here ''~~a~~''(''x'')~~ is the ~~number of pairs (''u''~~,~~''v'') with ''u'' conjugate~~ to '~~'t'', ''v'' conjugate~~ to ~~''z'',~~ and ~~''x'' in the subgroup generated by ''uv''~~.		Next to the gaudy, unusual eyeglasses that storm users to turncock their eyes up and to the right, the raw Earned run average ?? 42 pct smaller than the final model, just bigger than a nonplus of gumwood ?? is practically understated. It comes in black, red, silver, or bronze, with tips for either your the right way or left hand spike. I wore unmatched for respective hours without any discomfort, and without the judgmental looks I once potential. Everyone today talks to themselves as they walking bolt down the street; Jawbone's actually offer unmatched of the to the lowest degree clumsy and ostentatious ways of doing so.

	~~{{harvtxt\|Harris\|1972\|loc=3.10}} gives the following more complicated version of the Thompson order~~ ~~formula for the case when ''G'' has more than two conjugacy classes of involution.~~		Of course, audio frequency character is withal paramount for a Bluetooth headset. The recently ERA supports wideband audio, pregnant everything from FaceTime calls to Skype conferences volition auditory sensation as proficient as they should; it testament also turn with HD Voice, so telephone set calls wish auditory sensation markedly punter as wellspring.<br><br>If you are you looking for more information regarding [http://batuiti.com/ shop] review our webpage.
	~~:<math>\|G\| = C_G(t)C_G(z) \sum_x\frac{a(x)}{C_G(x)}</math>~~
	~~where ''t'' and ''z'' are non-conjugate involutions~~, ~~the sum~~ is ~~over a set of representatives ''x''~~ for ~~the conjugacy classes of involutions, and ''~~a~~''(''x'') is the number of ordered pairs of involutions ''u''~~,~~''v'' such that ''u'' is conjugate~~ to ~~''t''~~, ~~''v'' is conjugate to ''z'', and ''x'' is the involution in the subgroup generated by ''tz''~~.

	~~==Proof==~~

	~~The Thompson order formula can be rewritten as~~

	:<~~math~~>~~\frac{\|G\|}{C_G(z)}\frac{\|G\|}{C_G(t)} = \sum_x a(x)\frac{\|G\|}{C_G(x)}~~ <~~/math~~>

	~~where as before the sum is over a set of representatives ''x''~~ for ~~the classes of involutions.~~
	The left hand side is the number of pairs on involutions (''u'',''v'') with ''u'' conjugate to ''t'', ''v'' conjugate to ''z''. The right hand side counts these pairs in classes, depending the class of the involution in the cyclic group generated by ''uv''. The key point is that ''uv'' has even order (as if it had odd order then ''u'' and ''v'' would be conjugate) and so the group it generates contains a unique involution ''x''.

	~~==References==~~

	*{{Citation \| last1=Aschbacher \| first1=Michael \| author1-link=Michael Aschbacher \| title=Finite group theory \| publisher=[[~~Cambridge University Press]] \| edition=2nd \| series=Cambridge Studies in Advanced Mathematics \| isbn=978-0-521-78145-9; 978-0-521-78675-1 \| id={{MathSciNet \| id = 1777008}} \| year=2000 \| volume=10}}~~
	*{{Citation \| last1=Brauer \| first1=R. \| author1-link=Richard Brauer \| last2=Fowler \| first2=K. A. \| title=On groups of even order \| url=http://~~www.jstor~~.~~org/stable~~/~~1970080 \| id={{MR\|0074414}} \| year=1955 \| journal=[[Annals of Mathematics\|Annals of Mathematics. Second Series]~~] ~~\| issn=0003-486X \| volume=62 \| pages=565–583}}~~
	*{{Citation \| last1=Harris \| first1=Morton E. \| title=A characterization of odd order extensions of the finite projective symplectic groups PSp(4,q) \| url=http://www.jstor.org/stable/1995724 \| id={{MR\|0286897}} \| year=1972 \| journal=[[Transactions of the American Mathematical Society]] \| issn=0002-9947 \| volume=163 \| pages=311–327}}
	*{{Citation \| last1=Held \| first1=Dieter \| title=The simple groups related to M₂₄ \| doi=10.1016/0021-8693(69)90074-X \| id=0249500 \| year=1969 \| journal=[[Journal of Algebra]] \| issn=0021-8693 \| volume=13 \| pages=253–296}}
	*{{Citation \| last1=Suzuki \| first1=Michio \| author1-link=Michio Suzuki \| title=Group theory. II \| publisher=[[Springer-Verlag]] \| location=Berlin, New York \| series=Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] \| isbn=978-0-387-10916-9 \| id={{MathSciNet \| id = 815926}} \| year=1986 \| volume=248}}
	~~[[Category:Finite groups]]~~

en>Monkbot: Fix CS1 deprecated date parameter errors

2014-01-29T00:46:45Z

Fix CS1 deprecated date parameter errors

← Older revision		Revision as of 02:46, 29 January 2014
Line 1:		Line 1:
	I am Peter and was born on 23 December 1977. My hobbies are Board sports and Fishkeeping.<br>xunjie 1998年に設立された当社のクマのBチー迷彩服ブランドの生産における長年の経験を運ぶ快適な品質のブランドの信念、		In mathematical finite group theory, the '''Thompson order formula''', introduced by [[John Griggs Thompson]] {{harv\|Held\|1969\|loc=p.279}}, gives a formula for the order of a finite group in terms of the centralizers of involutions, extending the results of {{harvtxt\|Brauer\|Fowler\|1955}}.
	~~安徽省委員会は手紙や人的資源と社会保障省が共同で労働集約型の中小企業のプロジェクトデータベースを確立するために、~~
	~~コンテストの旅行服のデザイナーに参加したことが理解される積極的に参加している。~~ [http://www.steadfast-hawaii.org/img/p/hot/chloe.php �� ؔ�� ] この香りは今それらをリストのギフトを参加したいです！ 746778481日：2013 -8-25午後04時05分16秒ミシェル·チェンは笑顔が常に大衆に呼びかけ、
	~~またはそのシングルはあまりにも特殊なバレンタインデーを祝うためのもの？バレンタインデー同行する誰もいない、~~
	~~日付：あまりにもノーマルあまりにも一般警察官の行き過ぎた後に2013年8月24日10時27分12秒、~~ [~~http://www.steadfast-hawaii.org/img/p/hot/chloe.php �� Хå� ��~~] ~~世界で二番目に大きいの大豆生産国であり、~~
	~~スイス西部ラ·ショー·ドから1924年の年間生産量の専門家とを用いて製造職人花の牙（ラショードフォン）旧車機械支援生産。~~
	~~結果は通常のL番号が正しい着用するだけでなく、[http://www.swisscrossbow.ch/html/jp/good/gaga.html ��ߥ�� rӋ �� ~~] ~~ダイヤモンドジュエリーの特に「熊手」の場合に遭遇したときに壊れやすい、~~
	~~具体的に温かく遠くからのゲストを受け取っ南平市の温州合成皮革産業協会、~~
	~~決勝は11月3日であると予想される、~~
	~~協会編み物中国繊維工業協会と中国、 [http://www~~.~~steadfast-hawaii~~.~~org/img/p/hot/chloe.<br><br>�� ؔ�� ]~~

	~~My homepage~~ [http://~~belpars~~.by/~~Files~~/~~Config~~/tp/~~new~~/~~best~~/~~toms~~.~~html TOMS スリッポンメンズ~~]		==Statement==

			If a finite group ''G'' has exactly two conjugacy classes of involutions with representatives ''t'' and ''z'', then the Thompson order formula {{harv\|Aschbacher\|2000\|loc=45.6}} {{harv\|Suzuki\|1986\|loc=5.1.7}} states

			:\|G\| = \|C<sub>''G''</sub>(''z'')\|''a''(''t'') + \|C<sub>''G''</sub>(''t'')\|''a''(''z'')

			Here ''a''(''x'') is the number of pairs (''u'',''v'') with ''u'' conjugate to ''t'', ''v'' conjugate to ''z'', and ''x'' in the subgroup generated by ''uv''.

			{{harvtxt\|Harris\|1972\|loc=3.10}} gives the following more complicated version of the Thompson order formula for the case when ''G'' has more than two conjugacy classes of involution.
			:<math>\|G\| = C_G(t)C_G(z) \sum_x\frac{a(x)}{C_G(x)}</math>
			where ''t'' and ''z'' are non-conjugate involutions, the sum is over a set of representatives ''x'' for the conjugacy classes of involutions, and ''a''(''x'') is the number of ordered pairs of involutions ''u'',''v'' such that ''u'' is conjugate to ''t'', ''v'' is conjugate to ''z'', and ''x'' is the involution in the subgroup generated by ''tz''.

			==Proof==

			The Thompson order formula can be rewritten as

			:<math>\frac{\|G\|}{C_G(z)}\frac{\|G\|}{C_G(t)} = \sum_x a(x)\frac{\|G\|}{C_G(x)} </math>

			where as before the sum is over a set of representatives ''x'' for the classes of involutions.
			The left hand side is the number of pairs on involutions (''u'',''v'') with ''u'' conjugate to ''t'', ''v'' conjugate to ''z''. The right hand side counts these pairs in classes, depending the class of the involution in the cyclic group generated by ''uv''. The key point is that ''uv'' has even order (as if it had odd order then ''u'' and ''v'' would be conjugate) and so the group it generates contains a unique involution ''x''.

			==References==

			*{{Citation \| last1=Aschbacher \| first1=Michael \| author1-link=Michael Aschbacher \| title=Finite group theory \| publisher=[[Cambridge University Press]] \| edition=2nd \| series=Cambridge Studies in Advanced Mathematics \| isbn=978-0-521-78145-9; 978-0-521-78675-1 \| id={{MathSciNet \| id = 1777008}} \| year=2000 \| volume=10}}
			*{{Citation \| last1=Brauer \| first1=R. \| author1-link=Richard Brauer \| last2=Fowler \| first2=K. A. \| title=On groups of even order \| url=http://www.jstor.org/stable/1970080 \| id={{MR\|0074414}} \| year=1955 \| journal=[[Annals of Mathematics\|Annals of Mathematics. Second Series]] \| issn=0003-486X \| volume=62 \| pages=565–583}}
			*{{Citation \| last1=Harris \| first1=Morton E. \| title=A characterization of odd order extensions of the finite projective symplectic groups PSp(4,q) \| url=http://www.jstor.org/stable/1995724 \| id={{MR\|0286897}} \| year=1972 \| journal=[[Transactions of the American Mathematical Society]] \| issn=0002-9947 \| volume=163 \| pages=311–327}}
			*{{Citation \| last1=Held \| first1=Dieter \| title=The simple groups related to M₂₄ \| doi=10.1016/0021-8693(69)90074-X \| id=0249500 \| year=1969 \| journal=[[Journal of Algebra]] \| issn=0021-8693 \| volume=13 \| pages=253–296}}
			*{{Citation \| last1=Suzuki \| first1=Michio \| author1-link=Michio Suzuki \| title=Group theory. II \| publisher=[[Springer-Verlag]] \| location=Berlin, New York \| series=Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] \| isbn=978-0-387-10916-9 \| id={{MathSciNet \| id = 815926}} \| year=1986 \| volume=248}}
			[[Category:Finite groups]]

en>Helpful Pixie Bot: ISBNs (Build KE)

2012-05-10T22:21:52Z

ISBNs (Build KE)

New page

I am Peter and was born on 23 December 1977. My hobbies are Board sports and Fishkeeping.<br>xunjie 1998年に設立された当社のクマのBチー迷彩服ブランドの生産における長年の経験を運ぶ快適な品質のブランドの信念、
安徽省委員会は手紙や人的資源と社会保障省が共同で労働集約型の中小企業のプロジェクトデータベースを確立するために、
コンテストの旅行服のデザイナーに参加したことが理解される積極的に参加している。 [http://www.steadfast-hawaii.org/img/p/hot/chloe.php �� ؔ�� ] この香りは今それらをリストのギフトを参加したいです！ 746778481日：2013 -8-25午後04時05分16秒ミシェル·チェンは笑顔が常に大衆に呼びかけ、
またはそのシングルはあまりにも特殊なバレンタインデーを祝うためのもの？バレンタインデー同行する誰もいない、
日付：あまりにもノーマルあまりにも一般警察官の行き過ぎた後に2013年8月24日10時27分12秒、 [http://www.steadfast-hawaii.org/img/p/hot/chloe.php �� Хå� ��] 世界で二番目に大きいの大豆生産国であり、
スイス西部ラ·ショー·ドから1924年の年間生産量の専門家とを用いて製造職人花の牙（ラショードフォン）旧車機械支援生産。
結果は通常のL番号が正しい着用するだけでなく、[http://www.swisscrossbow.ch/html/jp/good/gaga.html ��ߥ�� rӋ �� ] ダイヤモンドジュエリーの特に「熊手」の場合に遭遇したときに壊れやすい、
具体的に温かく遠くからのゲストを受け取っ南平市の温州合成皮革産業協会、
決勝は11月3日であると予想される、
協会編み物中国繊維工業協会と中国、 [http://www.steadfast-hawaii.org/img/p/hot/chloe.<br><br>�� ؔ�� ]

My homepage [http://belpars.by/Files/Config/tp/new/best/toms.html TOMS スリッポンメンズ]