Geometric invariant theory: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older edit
en>Crasshopper
mNo edit summary
en>TakuyaMurata
 
Line 1: Line 1:
{{refimprove|date=October 2009}}
<br><br>I woke up last week  and noticed - Now I have also been solitary for some time and after much intimidation from buddies I now locate myself registered for web dating. They guaranteed me that there are lots of interesting, sweet and normal individuals to meet up, therefore here goes the message!<br>I make an effort to keep as physically fit as possible staying at the fitness center many times per week. I appreciate my sports and make an effort to play or watch while many a possible. Being wintertime I shall frequently at Hawthorn matches. Note: In case that you considered shopping a sport I do not mind, I have seen the carnage of  how to meet luke bryan ([http://www.hotelsedinburgh.org http://www.hotelsedinburgh.org]) wrestling matches at stocktake sales.<br>My  concert tickets luke bryan ([http://lukebryantickets.flicense.com http://lukebryantickets.flicense.com]) household and [http://www.Encyclopedia.com/searchresults.aspx?q=friends friends] are awe-inspiring and spending some time with them at [http://en.search.Wordpress.com/?q=tavern+gigs tavern gigs] or dishes is obviously critical. As I come to realize that one can do not have a decent conversation with all the sound I haven't ever been in to dance clubs. I likewise have 2 very adorable and undoubtedly cheeky puppies who are always enthusiastic to meet new folks.<br><br>Also visit my web site - [http://www.senatorwonderling.com Cheap Tickets To Luke Bryan]
In [[mathematics]], a '''quasisimple group''' (also known as a '''covering group''') is a [[group (mathematics)|group]] that is a [[perfect group|perfect]] [[Central extension (mathematics)|central extension]] ''E'' of a [[simple group]] ''S''.  In other words, there is a [[short exact sequence]]
 
:1 &rarr; ''Z''(''E'') &rarr; ''E'' &rarr; ''S'' &rarr; 1
 
such that ''E'' = [''E'', ''E''], where ''Z''(''E'') denotes the [[Center (group theory)|center]] of ''E'' and [, ] denotes the [[commutator]].<ref>I. Martin Isaacs, ''Finite group theory'' (2008), p. 272.</ref>
 
Equivalently, a group is quasisimple if it is isomorphic to its [[commutator subgroup]] and its [[inner automorphism|inner automorphism group]] Inn(''G'') (its [[quotient]] by its center) is simple; due to [[Perfect_group#Grün's lemma|Grün's lemma]], Inn(''G'') must be [[non-abelian group|non-abelian]]. All non-abelian simple groups are quasisimple.
 
The [[subnormal subgroup|subnormal]] quasisimple subgroups of a group control the structure of a finite [[insoluble group]] in much the same way as the minimal [[normal subgroup]]s of a finite [[soluble group]] do, and so are given a name, [[component (group theory)|component]]. 
 
The subgroup generated by the subnormal quasisimple subgroups is called the '''layer''', and along with the minimal normal soluble subgroups generates a subgroup called the [[generalized Fitting subgroup]].
 
The quasisimple groups are often studied alongside the simple groups and groups related to their [[automorphism group]]s, the [[almost simple group]]s. The [[representation theory of finite groups|representation theory]] of the quasisimple groups is nearly identical to the [[projective representation|projective representation theory]] of the simple groups.
 
==Examples==
The [[covering groups of the alternating and symmetric groups|covering groups of the alternating groups]] are quasisimple but not simple, for <math>n \geq 5.</math>
 
==See also==
* [[Almost simple group]]
* [[Schur multiplier]]
* [[Semisimple group]]
 
==References==
* {{ cite book | last=Aschbacher | first=Michael | title=Finite Group Theory | publisher=[[Cambridge University Press]] | year=2000 | isbn=0-521-78675-4 | zbl=0997.20001 }}
 
==External links==
*http://mathworld.wolfram.com/QuasisimpleGroup.html
 
==Notes==
{{Reflist}}
 
[[Category:Group theory]]
[[Category:Properties of groups]]
 
 
{{Abstract-algebra-stub}}

Latest revision as of 15:42, 10 January 2015



I woke up last week and noticed - Now I have also been solitary for some time and after much intimidation from buddies I now locate myself registered for web dating. They guaranteed me that there are lots of interesting, sweet and normal individuals to meet up, therefore here goes the message!
I make an effort to keep as physically fit as possible staying at the fitness center many times per week. I appreciate my sports and make an effort to play or watch while many a possible. Being wintertime I shall frequently at Hawthorn matches. Note: In case that you considered shopping a sport I do not mind, I have seen the carnage of how to meet luke bryan (http://www.hotelsedinburgh.org) wrestling matches at stocktake sales.
My concert tickets luke bryan (http://lukebryantickets.flicense.com) household and friends are awe-inspiring and spending some time with them at tavern gigs or dishes is obviously critical. As I come to realize that one can do not have a decent conversation with all the sound I haven't ever been in to dance clubs. I likewise have 2 very adorable and undoubtedly cheeky puppies who are always enthusiastic to meet new folks.

Also visit my web site - Cheap Tickets To Luke Bryan

Retrieved from "https://en.formulasearchengine.com/index.php?title=Geometric_invariant_theory&oldid=239282"