WORHP - Revision history

en>Faizhaider: clean up using AWB

2014-09-14T10:39:32Z

clean up using AWB

← Older revision		Revision as of 12:39, 14 September 2014
Line 1:		Line 1:
	~~In algebra~~, ~~more specifically [[group theory]]~~, ~~a ''p''-'''elementary group''' is a [[direct product of groups\|direct product]] of a finite [[cyclic group]] of order relatively prime to ''p''~~ and ~~a [[p-group\|''p''-group]]. A finite group is an elementary group if it is ''p''-elementary for some prime number ''p''. An elementary group is [[nilpotent group\|nilpotent]]~~.		My name is Emmanuel and I am studying Architecture, Art, and Planning and Biology at Rinn / Austria.<br><br>Review my page - [https://www.rebelmouse.com/snobbishcuff2345/need-a-roof-look-no-further-th-775445702.html commercial roofing perth]

	[[Brauer's theorem on induced characters]] states that a character on a finite group is a linear combination with integer coefficients of characters [[induced character\|induced]] from elementary subgroups.

	~~More generally, a finite group ''G'' is called a ''p''-'''hyperelementary''' if it has the extension~~
	~~:<math>1 \longrightarrow C \longrightarrow G \longrightarrow P \longrightarrow 1</math>~~
	~~where~~ <~~math~~>C<~~/math~~> ~~is cyclic of order prime to ''p'' and ''P'' is a ''p''-group. Not every hyperelementary group is elementary: for instance the non-abelian group of order 6 is 2-hyperelementary, but not 2~~-~~elementary. The term "hyperelementary" was introduced {{Citation needed\|date=March 2011}} by G. Segal.~~

	~~==References==~~
	* Arthur Bartels, Wolfgang Lück, ''[~~http~~://~~wwwmath~~.~~uni-muenster~~.de/u/~~bartelsa/research/induction.pdf Induction Theorems and Isomorphism Conjectures for K~~- ~~and L~~-~~Theory'']~~
	* G. Segal, ''[http://archive.numdam.org/ARCHIVE/PMIHES/PMIHES_1968__34_/PMIHES_1968__34__113_0/PMIHES_1968__34__113_0.pdf The representation-~~ring of a compact Lie group]''~~
	* J.P. Serre, "Linear representations of finite groups". Graduate Texts in Mathematics, vol. 42, Springer-~~Verlag, New York, Heidelberg, Berlin, 1977,~~

	~~[[Category:Representation theory of finite groups]]~~


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

en>Fbahr: Added {{Mathematical optimization software}} template

2013-12-09T17:28:34Z

Added {{Mathematical optimization software}} template

← Older revision		Revision as of 19:28, 9 December 2013
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			[[Brauer's theorem on induced characters]] states that a character on a finite group is a linear combination with integer coefficients of characters [[induced character\|induced]] from elementary subgroups.

			More generally, a finite group ''G'' is called a ''p''-'''hyperelementary''' if it has the extension
			:<math>1 \longrightarrow C \longrightarrow G \longrightarrow P \longrightarrow 1</math>
			where <math>C</math> is cyclic of order prime to ''p'' and ''P'' is a ''p''-group. Not every hyperelementary group is elementary: for instance the non-abelian group of order 6 is 2-hyperelementary, but not 2-elementary. The term "hyperelementary" was introduced {{Citation needed\|date=March 2011}} by G. Segal.

			==References==
			* Arthur Bartels, Wolfgang Lück, ''[http://wwwmath.uni-muenster.de/u/bartelsa/research/induction.pdf Induction Theorems and Isomorphism Conjectures for K- and L-Theory'']
			* G. Segal, ''[http://archive.numdam.org/ARCHIVE/PMIHES/PMIHES_1968__34_/PMIHES_1968__34__113_0/PMIHES_1968__34__113_0.pdf The representation-ring of a compact Lie group]''
			* J.P. Serre, "Linear representations of finite groups". Graduate Texts in Mathematics, vol. 42, Springer-Verlag, New York, Heidelberg, Berlin, 1977,

			[[Category:Representation theory of finite groups]]


			{{Abstract-algebra-stub}}

en>Redrose64: /* Development */ dab

2012-06-28T21:49:06Z

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