Difference between revisions of "Subgroup with abelianization of maximum order"

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(Created page with '==Definition== Let <math>P</math> be a group of prime power order. A subgroup <math>B</math> of <math>P</math> is termed a '''subgroup with abelianization of maximum ord…')
 
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Let <math>P</math> be a [[group of prime power order]]. A [[subgroup]] <math>B</math> of <math>P</math> is termed a '''subgroup with abelianization of maximum order''' if the [[order of a group|order]] of the [[abelianization]] of <math>B</math> (i.e., the quotient of <math>B</math> by its [[commutator subgroup]]) is greater than or equal to the order of the abelianization of any subgroup of <math>P</math>.
 
Let <math>P</math> be a [[group of prime power order]]. A [[subgroup]] <math>B</math> of <math>P</math> is termed a '''subgroup with abelianization of maximum order''' if the [[order of a group|order]] of the [[abelianization]] of <math>B</math> (i.e., the quotient of <math>B</math> by its [[commutator subgroup]]) is greater than or equal to the order of the abelianization of any subgroup of <math>P</math>.
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==Relation with other properties==
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===Stronger properties===
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* [[Weaker than::Minimal subgroup with abelianization of maximum order]]

Revision as of 23:42, 26 July 2009

Definition

Let P be a group of prime power order. A subgroup B of P is termed a subgroup with abelianization of maximum order if the order of the abelianization of B (i.e., the quotient of B by its commutator subgroup) is greater than or equal to the order of the abelianization of any subgroup of P.

Relation with other properties

Stronger properties