Fusion system-relatively weakly closed subgroup: Difference between revisions
(Created page with '{{wikilocal}} {{prime-parametrized subgroup property}} ==Definition== Suppose <math>G</math> is a group of prime power order, i.e., a finite <math>p</math>-group for some [[…') |
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===Stronger properties=== | ===Stronger properties=== | ||
* [[Weaker than::Isomorph-normal coprime automorphism-invariant subgroup]]: {{proofat|[[Isomorph-normal coprime automorphism-invariant implies weakly closed for any fusion system]]}} | * [[Weaker than::Isomorph-normal coprime automorphism-invariant subgroup of group of prime power order]]: {{proofat|[[Isomorph-normal coprime automorphism-invariant implies weakly closed for any fusion system]]}} | ||
** [[Weaker than::Isomorph-normal characteristic subgroup]] | ** [[Weaker than::Isomorph-normal characteristic subgroup of group of prime power order]] | ||
** [[Weaker than::Coprime automorphism-invariant maximal subgroup of group of prime power order]] | ** [[Weaker than::Coprime automorphism-invariant maximal subgroup of group of prime power order]] | ||
** [[Weaker than::Isomorph-free subgroup of group of prime power order]] | |||
* [[Weaker than::Fusion system-relatively strongly closed subgroup]] | |||
** [[Weaker than::Subisomorph-containing subgroup of group of prime power order]] | |||
===Weaker properties=== | ===Weaker properties=== | ||
* [[Stronger than::Sylow-relatively weakly closed subgroup]] | * [[Stronger than::Sylow-relatively weakly closed subgroup]] | ||
Revision as of 14:59, 8 August 2009
BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
The article defines a subgroup property, where the definition may be in terms of a particular prime number that serves as parameter
View other prime-parametrized subgroup properties | View all subgroup properties
Definition
Suppose is a group of prime power order, i.e., a finite -group for some prime number . A subgroup of is termed a fusion system-relatively weakly closed subgroup if is a weakly closed subgroup for any fusion system on .
Relation with other properties
Stronger properties
- Isomorph-normal coprime automorphism-invariant subgroup of group of prime power order: For full proof, refer: Isomorph-normal coprime automorphism-invariant implies weakly closed for any fusion system
- Fusion system-relatively strongly closed subgroup