Commuting product: Difference between revisions

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{{subgroup-defining function}}
#redirect [[Layer]]
 
==Definition==
 
===Symbol-free definition===
 
The '''commuting product''' of a group is defined as the product of all its [[component]]s.
 
===Definition with symbols===
 
The '''commuting product''' of a group <math>G</math>, sometimes denoted as <math>E(G)</math>, is defined as the product of all subgroups <math>H</math> of <math>G</math> that are [[quasisimple group|quasisimple]] as abstract groups and [[subnormal subgroup|subnormal]] as subgroups of <math>G</math>.
 
==Relation with other subgroup-defining functions==
 
* [[Generalized Fitting subgroup]] is defined as the product of the commuting product and the [[Fitting subgroup]].

Latest revision as of 23:19, 7 May 2008

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