# Isomorph-normal coprime automorphism-invariant implies weakly closed for any fusion system

From Groupprops

(Redirected from Isomorph-normal coprime automorphism-invariant implies fusion system-relatively weakly closed)

ANALOGY: This is an analogue in fusion systems of a fact encountered in group. The old fact is: isomorph-normal coprime automorphism-invariant of Sylow implies weakly closed.

View other analogues of isomorph-normal coprime automorphism-invariant of Sylow implies weakly closed|View other analogues from group to fusion system (OR, View as a tabulated list)

## Statement

Suppose is a group of prime power order, and is an Isomorph-normal coprime automorphism-invariant subgroup (?) of , i.e., is an Isomorph-normal subgroup (?) of and it is also coprime automorphism-invariant in . In particular, is an Isomorph-normal coprime automorphism-invariant subgroup of group of prime power order (?).

Then, for any fusion system on , is a weakly closed subgroup for .