Finite normal subgroup: Difference between revisions
(New page: {{group-subgroup property conjunction|normal subgroup|finite group}} ==Definition== A subgroup of a group is termed a '''finite normal subgroup''' if it is [[finite group|finite ...) |
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* [[Weaker than::Finite central subgroup]] | * [[Weaker than::Finite central subgroup]] | ||
* [[Weaker than::Finite characteristic subgroup]] | * [[Weaker than::Finite characteristic subgroup]] | ||
* [[Weaker than::Normal subgroup of finite group]] | |||
===Weaker properties=== | ===Weaker properties=== | ||
Revision as of 14:19, 26 March 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): finite group
View a complete list of such conjunctions
Definition
A subgroup of a group is termed a finite normal subgroup if it is finite as a group and normal as a subgroup.
Relation with other properties
Stronger properties
- Normal subgroup of prime order
- Finite central subgroup
- Finite characteristic subgroup
- Normal subgroup of finite group
Weaker properties
- Amalgam-characteristic subgroup: For full proof, refer: Finite normal implies amalgam-characteristic
- Finitely generated normal subgroup
- Normal closure of finite subset
- Finite subnormal subgroup