Vipul: New page: ==Definition== Suppose $P$ is a defining ingredient::group of prime power order. A subgroup $K$ of $P$ is termed a '''center of critical subgroup''' o...

2008-10-12T13:29:38Z

New page: ==Definition== Suppose <math>P</math> is a defining ingredient::group of prime power order. A subgroup <math>K</math> of <math>P</math> is termed a '''center of critical subgroup''' o...

New page

==Definition==

Suppose <math>P</math> is a [[defining ingredient::group of prime power order]]. A subgroup <math>K</math> of <math>P</math> is termed a '''center of critical subgroup''' of <math>P</math> if there exists a [[defining ingredient::critical subgroup]] <math>C</math> of <math>G</math> such that <math>Z(C) = K</math>.

==Relation with other properties==

===Stronger properties===

* [[Maximal among Abelian characteristic subgroups]] (for a [[group of prime power order]])

===Weaker properties===

* [[Stronger than::Abelian characteristic subgroup]]
* [[Stronger than::Subgroup containing the center]]

Center of critical subgroup - Revision history

Vipul: New page: ==Definition== Suppose P is a defining ingredient::group of prime power order. A subgroup K of P is termed a '''center of critical subgroup''' o...

Vipul: New page: ==Definition== Suppose $P$ is a defining ingredient::group of prime power order. A subgroup $K$ of $P$ is termed a '''center of critical subgroup''' o...