Multivariate gamma function - Revision history

en>Bilgrau: Abbreviated trace to the more common tr.

2014-09-08T10:17:07Z

Abbreviated trace to the more common tr.

← Older revision		Revision as of 12:17, 8 September 2014
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	~~In [[mathematics]], the~~ '~~''Schreier refinement theorem''' of [[group theory]] states that any two [[subnormal series]] of [[subgroup]]~~s of a ~~given group have equivalent refinements, where two series are equivalent if there~~ is ~~a bijection between their factor groups that sends each factor group~~ to ~~an isomorphic one~~.		The writer is known as Wilber Pegues. It's not a typical thing but what I like doing is to climb but I don't have the time lately. Alaska is the only location I've been residing in but now I'm considering other options. I am an invoicing officer and I'll be promoted quickly.<br><br>Here is my weblog - love psychics - [http://rv4x4.com/?q=tips-about-hobbies-easy-follow-along my latest blog post],

	~~The theorem~~ is ~~named after~~ the ~~[[Austria]]n [[mathematician]] [[Otto Schreier]] who proved it~~ in ~~1928~~. ~~It provides~~ an ~~elegant proof of the [[Jordan–Hölder theorem]]~~. ~~It is often proved using the [[Zassenhaus lemma]].~~

	~~== Example ==~~

	~~Consider <math>\mathbb{Z}/(2) \times S_3</math>, where~~ <~~math~~>~~S_3~~<~~/math~~> is ~~the~~ [~~[symmetric group of degree 3]]. There are subnormal series~~

	~~: <math>\{[0]\} \times \{\operatorname{id}\} \; \triangleleft \; \mathbb{Z}/(2) \times \{\operatorname{id}\} \; \triangleleft \; \mathbb{Z}/(2) \times S_3,</math>~~
	: ~~<math>\{[0]\} \times \{\operatorname{id}\} \; \triangleleft \; \{[0]\} \times S_3 \; \triangleleft \; \mathbb{Z}~~/~~(2) \times S_3.</math>~~

	~~<math>S_3</math> contains the normal subgroup <math>A_3<~~/~~math>~~. ~~Hence these have refinements~~

	: <math>\{[0]\} \times \{\operatorname{id}\} \; \triangleleft \; \mathbb{Z}/(2) \times \{\operatorname{id}\} \; \triangleleft \; \mathbb{Z}/(2) \times A_3 \; \triangleleft \; \mathbb{Z}/(2) \times S_3</math>

	~~with factor groups isomorphic to <math>(\mathbb{Z}/(2), A_3, \mathbb{Z}/(2))</math> and~~

	~~: <math>\{[0]\} \times \{\operatorname{id}\} \; \triangleleft \; \{[0]\} \times A_3 \; \triangleleft \; \{[0]\} \times S_3 \; \triangleleft \; \mathbb{Z}~~/~~(2) \times S_3</math>~~

	~~with factor groups isomorphic to <math>(A_3, \mathbb{Z}/(2), \mathbb{Z}/(2))</math>.~~

	=~~= References ==~~
	*{{cite book \| author=Rotman, Joseph \| title=An introduction to the theory of groups \| location=New York \| publisher=Springer-~~Verlag \| year=1994 \| isbn=0~~-~~387~~-~~94285~~-~~8}}~~

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

	~~{{Abstract-algebra-stub}}~~

en>The Disambiguator: positive-definite matrix

2013-04-14T11:43:51Z

positive-definite matrix

← Older revision		Revision as of 13:43, 14 April 2013
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	~~Wilber Berryhill~~ is ~~what his wife loves~~ to ~~contact him and he completely enjoys this name~~. ~~Since he was 18 he's been working as~~ an ~~info officer but he plans on changing it~~. ~~My spouse and I reside in Mississippi and I love every day living here~~. ~~The preferred pastime for him and his kids~~ is ~~to play lacross and he would by no means give it up~~.<br><br>~~Feel free to surf to my web site~~; ~~certified psychics~~ ([~~http~~://~~beta.cinevault.com~~/~~profile~~.~~php?u~~=~~LoCostanti beta.cinevault.com~~])		In [[mathematics]], the '''Schreier refinement theorem''' of [[group theory]] states that any two [[subnormal series]] of [[subgroup]]s of a given group have equivalent refinements, where two series are equivalent if there is a bijection between their factor groups that sends each factor group to an isomorphic one.

			The theorem is named after the [[Austria]]n [[mathematician]] [[Otto Schreier]] who proved it in 1928. It provides an elegant proof of the [[Jordan–Hölder theorem]]. It is often proved using the [[Zassenhaus lemma]].

			== Example ==

			Consider <math>\mathbb{Z}/(2) \times S_3</math>, where <math>S_3</math> is the [[symmetric group of degree 3]]. There are subnormal series

			: <math>\{[0]\} \times \{\operatorname{id}\} \; \triangleleft \; \mathbb{Z}/(2) \times \{\operatorname{id}\} \; \triangleleft \; \mathbb{Z}/(2) \times S_3,</math>
			: <math>\{[0]\} \times \{\operatorname{id}\} \; \triangleleft \; \{[0]\} \times S_3 \; \triangleleft \; \mathbb{Z}/(2) \times S_3.</math>

			<math>S_3</math> contains the normal subgroup <math>A_3</math>. Hence these have refinements

			: <math>\{[0]\} \times \{\operatorname{id}\} \; \triangleleft \; \mathbb{Z}/(2) \times \{\operatorname{id}\} \; \triangleleft \; \mathbb{Z}/(2) \times A_3 \; \triangleleft \; \mathbb{Z}/(2) \times S_3</math>

			with factor groups isomorphic to <math>(\mathbb{Z}/(2), A_3, \mathbb{Z}/(2))</math> and

			: <math>\{[0]\} \times \{\operatorname{id}\} \; \triangleleft \; \{[0]\} \times A_3 \; \triangleleft \; \{[0]\} \times S_3 \; \triangleleft \; \mathbb{Z}/(2) \times S_3</math>

			with factor groups isomorphic to <math>(A_3, \mathbb{Z}/(2), \mathbb{Z}/(2))</math>.

			== References ==
			*{{cite book \| author=Rotman, Joseph \| title=An introduction to the theory of groups \| location=New York \| publisher=Springer-Verlag \| year=1994 \| isbn=0-387-94285-8}}

			[[Category:Theorems in group theory]]

			{{Abstract-algebra-stub}}

76.120.181.41: edit

2012-09-01T22:49:26Z

edit

New page

Wilber Berryhill is what his wife loves to contact him and he completely enjoys this name. Since he was 18 he's been working as an info officer but he plans on changing it. My spouse and I reside in Mississippi and I love every day living here. The preferred pastime for him and his kids is to play lacross and he would by no means give it up.<br><br>Feel free to surf to my web site; certified psychics ([http://beta.cinevault.com/profile.php?u=LoCostanti beta.cinevault.com])