Antimatter comet - Revision history

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2014-10-10T22:49:43Z

Ball lightning

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	~~In mathematical finite group theory, the '''Dempwolff group''' is a [[finite group]] of order 319979520 = 2~~<~~sup~~>15<~~/sup~~>~~·3<sup>2</sup>·5·7·31, that is~~ the ~~unique nonsplit extension <math>2^{5\~~,~~.}\mathrm{GL}_{5}(\mathbb{F}_{2})<~~/~~math> of <math>\mathrm{GL}_{5}(\mathbb{F}_{2})<~~/~~math> by its natural module of order <math>2^5<~~/~~math>. The uniqueness~~ of ~~such a nonsplit extension was shown by {{harvtxt\|Dempwolff\|1972}},~~ and the ~~existence by {{harvtxt\|Thompson\|1976}}, who showed using some computer calculations of {{harvtxt\|Smith\|1976}}~~ that ~~the Dempwolff group~~ is ~~contained in the compact Lie group <math>E_{8}</math> as the subgroup fixing~~ a ~~certain lattice in~~ the ~~Lie algebra~~ of ~~<math>E_{8}</math>,~~ and ~~is also contained~~ in the ~~[[Thompson sporadic group]] (~~the ~~full automorphism group~~ of ~~this lattice) as a maximal subgroup~~.		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These radical elements sought black separation and social change by violent means. And so in a time when there was tremendous turmoil in the country because of the violence in Vietnam and on the streets of America because of that social strife, The Black Panthers and other fringe groups sewed fear and hatred in response to racism which at times made it more difficult to achieve long lasting change.<br><br>But there is good to be seen even in some of the darker elements of black history and the leadership who looked to find the best way forward for African Americans. Sometimes it is necessary for the radical elements to make themselves known so reasonable [http://tinyurl.com/kecvhhb http://tinyurl.com/kecvhhb] members of a community can know the outer limits and find compromise. 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So if black youth took pride and courage to face their own circumstances from the bold stance of leaders who, albeit radically, said loud that black America was now going to be a force to be reckoned with, the resultant call to action to the black community produced many more positive effects than negative ones. The fringe voice does speak what is in people's hearts and by getting that anger and [http://tinyurl.com/kecvhhb discount ugg boots] frustration out, it became part of the movement. That energy could be captured and used for good instead of evil. And the end result was a movement that was energized for change and to make life better for all of black America. And that was what everybody wanted.<br><br>PPPPP 643arvinoor<br>arvinoor siregar<br>arvinoor siregar sh.<br>arvinoor siregar sh.mh.

	~~{{harvtxt\|Huppert\|1967\|loc=p.124}} showed that that~~ ~~any extension of <math>\mathrm{GL}_{n}(\mathbb{F}_{q})</math> by its natural module <math>\mathbb{F}_{q}^{n}</math> splits if <math>q>2</math>, and {{harvtxt\|Dempwolff\|1973}} showed~~ that it ~~also splits if~~ <~~math~~>n<~~/math~~> is ~~not 3, 4, or 5~~, and in ~~each of these three cases there is just one non-split extension~~. ~~These three~~ ~~nonsplit extensions can be constructed~~ as ~~follows~~:
	*The nonsplit extension <math>2^{3\,.~~}\mathrm{GL}_{3}(\mathbb{F}_{2})<~~/~~math> is a maximal subgroup of the [[Chevalley group]~~] <~~math~~>~~G_{2}(\mathbb{F}_{3})~~<~~/math~~>.
	*The nonsplit extension <math>2^{4\,~~.}\mathrm{GL}_{4}(\mathbb{F}_{2})</math> is a maximal subgroup~~ of the ~~sporadic [[Conway group]] Co<sub>3</sub>~~.
	*The nonsplit extension <math>2^{5\,~~.}\mathrm{GL}_{5}(\mathbb{F}_{2})</math> is a maximal subgroup~~ of the [~~[Thompson sporadic group]] Th.~~

	~~==References==~~
	*{{Citation \| last1=Dempwolff \| first1=Ulrich \| title=On extensions of an elementary abelian group of order 2<sup>5</sup> by GL(5,2) \| url=http://www.~~numdam~~.~~org~~/~~item~~?id=~~RSMUP_1972__48__359_0 \| mr~~=~~0393276 \| year~~=~~1972 \| journal~~=~~Rendiconti del Seminario Matematico della Università di Padova~~. ~~The Mathematical Journal~~ of the ~~University~~ of ~~Padova \| issn=0041-8994 \| volume=48 \| pages=359–364}}~~
	*{{Citation \| last1=Dempwolff \| first1=Ulrich \| title=On the ~~second cohomology of GL(n,2) \| doi=10~~.~~1017/S1446788700014221 \| mr=0357639 \| year=1973 \| journal=Australian Mathematical Society. Journal. Series A. Pure Mathematics~~ and ~~Statistics \| issn=0263-6115 \| volume=16 \| pages=207–209}}~~
	*{{Citation \| last1=Griess \| first1=Robert L. ~~\| title=On~~ a ~~subgroup~~ of ~~order 2<sup>15</sup> . ¦GL(5~~,~~2)¦~~ in E<~~sub~~>8<~~/sub~~>~~(C),~~ the ~~Dempwolff group~~ and ~~Aut(D<sub>8<~~/~~sub>°D<sub>8<~~/~~sub>°D<sub>8<~~/~~sub>) \| doi=10~~.~~1016~~/~~0021-8693(76)90097-1 \| mr=0407149 \| year=1976 \| journal=[[Journal~~ of ~~Algebra]] \| issn=0021-8693 \| volume=40 \| issue=1 \| pages=271–279}}~~
	*{{Citation \| last1=Huppert \| first1=Bertram \| author1-link=Bertram Huppert \| title=Endliche Gruppen \| publisher=[~~[Springer-Verlag~~]~~] \| location=Berlin~~, ~~New York \| language=German \| isbn=978-3-540-03825-2 \| oclc=527050 \| mr=0224703 \| year=1967}}~~
	*{{Citation \| last1=Smith \| first1=P. ~~E. \| title=A simple subgroup of M? and E~~<~~sub~~>8<~~/sub~~>~~(3) \| doi=10.1112~~/~~blms~~/8.2.~~161~~ ~~\| mr=0409630 \| year=1976 \| journal=The Bulletin~~ of the ~~London Mathematical Society \| issn=0024-6093 \| volume=8 \| issue=2 \| pages=161–165}}~~
	*{{Citation \| last1=Thompson \| first1=John G. ~~\| author1-link=John G~~. ~~Thompson \| title=A conjugacy theorem~~ for ~~E<sub>8</sub> \| doi=10~~.~~1016/0021-8693(76)90235-0 \| mr=0399193 \| year=1976 \| journal=[[Journal~~ of ~~Algebra]] \| issn=0021-8693 \| volume=38 \| issue=2 \| pages=525–530}}~~

	~~==External links==~~
	*[http://~~brauer~~.~~maths~~.~~qmul~~.~~ac.uk/Atlas/v3/misc/25L52/ Dempwolff group] at~~ the ~~atlas~~ of ~~groups~~.

	~~[[Category:Finite groups]]~~

en>Monkbot: Fix CS1 deprecated date parameter errors

2014-01-14T01:07:14Z

Fix CS1 deprecated date parameter errors

← Older revision		Revision as of 03:07, 14 January 2014
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	~~Although African American artwork is standard as we speak within the United States~~, ~~this type of art owes its origins to~~ the ~~local art~~ of ~~Central and West Africa.~~<br>~~This artwork noticed progress between the seventeenth and the early nineteenth centuries. During this period~~, the ~~artwork took varied kinds, akin to ceramic vessels, wrought iron figures~~, ~~quilts and small drums~~. ~~This art type was additional popularized within the local markets of western European by artists, similar to Joshua Johnson~~ (~~painter from Baltimore~~) ~~and Scipio Moorhead~~ (~~engraver from New England~~).<br><br>~~Renaissance to Modern Day:~~ The ~~Journey~~ of ~~African American Art<br>Even after an extended~~ and ~~vibrant history~~, the ~~African American art~~ group ~~nonetheless wants assist~~ in the ~~modern day world. 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Johnson, Palmer Hayden, Richmond Barthe and Hale Woodruff, to name a~~ [~~http://tinyurl.com/kecvhhb ugg boots sale~~] ~~few~~. ~~In an attempt to advertise black artists, William~~ E. ~~Harmon established the Harmon Basis, which supported numerous artists via its annually held exhibitions~~ and ~~the Harmon Award.~~<br>~~Another attempt came in 1933, when the Public Works of Art Mission was introduced by the US Treasury Department~~. ~~Nonetheless, this [http:~~//~~tinyurl~~.~~com/kecvhhb cheap ugg boots] attempt wasn't too successful~~. ~~It was after World Conflict II (1939~~ - ~~1945) that African American artwork started getting worldwide recognition, with exhibitions held in cities comparable to Paris, Amsterdam, and others~~.<br><br>~~Right now, this art type explores varied fields, comparable to violence, sexuality, gender, race and identity~~.~~<br>African American Art Requires Help Even Today<br>However, the latest White Home campaign to carry back the wide range~~ of ~~this art form has been profitable in popularizing this~~ [http://~~Www~~.~~Encyclopedia~~.~~com~~/~~searchresults.aspx?q=artwork+form artwork form~~]~~. But there is a a lot wider scope for black art other than~~ the ~~expositions, auction costs and demanding reviews. Right this moment, this art kind wants distinguished advocacy so that it will possibly easily attain out to people in each nook~~ of ~~this world~~.Try the most important assortment of unique African/African American artworks, sculptures, collectible figurines, clothes, merchandise, books, DVDs, pictures and accessories at our on-line store.<br><br>Crafted by a few of the most famous artists, such as: ~~Thomas Blackshear, Charles Bibbss, Annie lee and WAK, these artifacts are a collector's delight.~~		In mathematical finite group theory, the '''Dempwolff group''' is a [[finite group]] of order 319979520 = 2<sup>15</sup>·3<sup>2</sup>·5·7·31, that is the unique nonsplit extension <math>2^{5\,.}\mathrm{GL}_{5}(\mathbb{F}_{2})</math> of <math>\mathrm{GL}_{5}(\mathbb{F}_{2})</math> by its natural module of order <math>2^5</math>. The uniqueness of such a nonsplit extension was shown by {{harvtxt\|Dempwolff\|1972}}, and the existence by {{harvtxt\|Thompson\|1976}}, who showed using some computer calculations of {{harvtxt\|Smith\|1976}} that the Dempwolff group is contained in the compact Lie group <math>E_{8}</math> as the subgroup fixing a certain lattice in the Lie algebra of <math>E_{8}</math>, and is also contained in the [[Thompson sporadic group]] (the full automorphism group of this lattice) as a maximal subgroup.

			{{harvtxt\|Huppert\|1967\|loc=p.124}} showed that that any extension of <math>\mathrm{GL}_{n}(\mathbb{F}_{q})</math> by its natural module <math>\mathbb{F}_{q}^{n}</math> splits if <math>q>2</math>, and {{harvtxt\|Dempwolff\|1973}} showed that it also splits if <math>n</math> is not 3, 4, or 5, and in each of these three cases there is just one non-split extension. These three nonsplit extensions can be constructed as follows:
			*The nonsplit extension <math>2^{3\,.}\mathrm{GL}_{3}(\mathbb{F}_{2})</math> is a maximal subgroup of the [[Chevalley group]] <math>G_{2}(\mathbb{F}_{3})</math>.
			*The nonsplit extension <math>2^{4\,.}\mathrm{GL}_{4}(\mathbb{F}_{2})</math> is a maximal subgroup of the sporadic [[Conway group]] Co<sub>3</sub>.
			*The nonsplit extension <math>2^{5\,.}\mathrm{GL}_{5}(\mathbb{F}_{2})</math> is a maximal subgroup of the [[Thompson sporadic group]] Th.

			==References==
			*{{Citation \| last1=Dempwolff \| first1=Ulrich \| title=On extensions of an elementary abelian group of order 2<sup>5</sup> by GL(5,2) \| url=http://www.numdam.org/item?id=RSMUP_1972__48__359_0 \| mr=0393276 \| year=1972 \| journal=Rendiconti del Seminario Matematico della Università di Padova. The Mathematical Journal of the University of Padova \| issn=0041-8994 \| volume=48 \| pages=359–364}}
			*{{Citation \| last1=Dempwolff \| first1=Ulrich \| title=On the second cohomology of GL(n,2) \| doi=10.1017/S1446788700014221 \| mr=0357639 \| year=1973 \| journal=Australian Mathematical Society. Journal. Series A. Pure Mathematics and Statistics \| issn=0263-6115 \| volume=16 \| pages=207–209}}
			*{{Citation \| last1=Griess \| first1=Robert L. \| title=On a subgroup of order 2<sup>15</sup> . ¦GL(5,2)¦ in E<sub>8</sub>(C), the Dempwolff group and Aut(D<sub>8</sub>°D<sub>8</sub>°D<sub>8</sub>) \| doi=10.1016/0021-8693(76)90097-1 \| mr=0407149 \| year=1976 \| journal=[[Journal of Algebra]] \| issn=0021-8693 \| volume=40 \| issue=1 \| pages=271–279}}
			*{{Citation \| last1=Huppert \| first1=Bertram \| author1-link=Bertram Huppert \| title=Endliche Gruppen \| publisher=[[Springer-Verlag]] \| location=Berlin, New York \| language=German \| isbn=978-3-540-03825-2 \| oclc=527050 \| mr=0224703 \| year=1967}}
			*{{Citation \| last1=Smith \| first1=P. E. \| title=A simple subgroup of M? and E<sub>8</sub>(3) \| doi=10.1112/blms/8.2.161 \| mr=0409630 \| year=1976 \| journal=The Bulletin of the London Mathematical Society \| issn=0024-6093 \| volume=8 \| issue=2 \| pages=161–165}}
			*{{Citation \| last1=Thompson \| first1=John G. \| author1-link=John G. Thompson \| title=A conjugacy theorem for E<sub>8</sub> \| doi=10.1016/0021-8693(76)90235-0 \| mr=0399193 \| year=1976 \| journal=[[Journal of Algebra]] \| issn=0021-8693 \| volume=38 \| issue=2 \| pages=525–530}}

			==External links==
			*[http://brauer.maths.qmul.ac.uk/Atlas/v3/misc/25L52/ Dempwolff group] at the atlas of groups.

			[[Category:Finite groups]]

46.177.106.159 at 04:37, 27 August 2012

2012-08-27T04:37:39Z

New page

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