Difference between revisions of "Class two normal subgroup"

From Groupprops
Jump to: navigation, search
(New page: {{group-subgroup property conjunction|normal subgroup|group of nilpotence class two}} ==Definition== A subgroup of a group is termed a '''class two normal subgroup''' if it is a ...)
 
 
(2 intermediate revisions by the same user not shown)
Line 5: Line 5:
 
A [[subgroup]] of a [[group]] is termed a '''class two normal subgroup''' if it is a [[normal subgroup]] and is also [[nilpotent group|nilpotent]], with nilpotence class at most two.
 
A [[subgroup]] of a [[group]] is termed a '''class two normal subgroup''' if it is a [[normal subgroup]] and is also [[nilpotent group|nilpotent]], with nilpotence class at most two.
  
 +
==Examples==
 +
 +
{{group-subgroup property conjunction see examples|normal subgroup|group of nilpotency class two}}
 
==Relation with other properties==
 
==Relation with other properties==
  
Line 13: Line 16:
 
* [[Weaker than::Critical subgroup]]
 
* [[Weaker than::Critical subgroup]]
 
* [[Weaker than::Class two characteristic subgroup]]
 
* [[Weaker than::Class two characteristic subgroup]]
 +
* [[Weaker than::Commutator-in-center subgroup]]
 +
* [[Weaker than::Aut-abelian normal subgroup]]
  
 
===Weaker properties===
 
===Weaker properties===
  
 
* [[Stronger than::Nilpotent normal subgroup]]
 
* [[Stronger than::Nilpotent normal subgroup]]

Latest revision as of 22:48, 2 November 2009

This article describes a property that arises as the conjunction of a subgroup property: normal subgroup with a group property (itself viewed as a subgroup property): group of nilpotence class two
View a complete list of such conjunctions

Definition

A subgroup of a group is termed a class two normal subgroup if it is a normal subgroup and is also nilpotent, with nilpotence class at most two.

Examples

VIEW: subgroups satisfying this property | subgroups dissatisfying property normal subgroup | subgroups dissatisfying property group of nilpotency class two
VIEW: Related subgroup property satisfactions | Related subgroup property dissatisfactions

Relation with other properties

Stronger properties

Weaker properties