Stabilizer groups
Content created by Fredrik Bakke, Jonathan Prieto-Cubides and Egbert Rijke.
Created on 2022-03-17.
Last modified on 2023-03-13.
module group-theory.stabilizer-groups where
Imports
open import foundation.dependent-pair-types open import foundation.identity-types open import foundation.universe-levels open import group-theory.group-actions open import group-theory.groups
Idea
Given a G-set X
, the stabilizer group at an element x
of X
is the subgroup
of elements g
of G
that keep x
fixed.
Definition
module _ {l1 l2 : Level} (G : Group l1) (X : Abstract-Group-Action G l2) where type-stabilizer-Abstract-Group-Action : type-Abstract-Group-Action G X → UU (l1 ⊔ l2) type-stabilizer-Abstract-Group-Action x = Σ (type-Group G) (λ g → Id (mul-Abstract-Group-Action G X g x) x)
Recent changes
- 2023-03-13. Jonathan Prieto-Cubides. More maintenance (#506).
- 2023-03-10. Fredrik Bakke. Additions to
fix-import
(#497). - 2023-03-09. Jonathan Prieto-Cubides. Add hooks (#495).
- 2023-03-07. Fredrik Bakke. Add blank lines between
<details>
tags and markdown syntax (#490). - 2023-03-07. Jonathan Prieto-Cubides. Show module declarations (#488).