Subgroup with abelianization of maximum order: Difference between revisions
(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…') |
No edit summary |
||
| Line 2: | Line 2: | ||
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>. | ||
==Relation with other properties== | |||
===Stronger properties=== | |||
* [[Weaker than::Minimal subgroup with abelianization of maximum order]] | |||
Revision as of 23:42, 26 July 2009
Definition
Let be a group of prime power order. A subgroup of is termed a subgroup with abelianization of maximum order if the order of the abelianization of (i.e., the quotient of by its commutator subgroup) is greater than or equal to the order of the abelianization of any subgroup of .