Fusion system-relatively weakly closed subgroup
From Groupprops
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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