Theorems · Definition · group theory
AddAction.stabilizer
(G : Type u_1) → {α : Type u_2} → [inst : AddGroup G] → [AddAction G α] → α → AddSubgroup GThe stabilizer of an element under an action, i.e. what sends the element to itself. An additive subgroup.
- Defined in
- Mathlib.GroupTheory.GroupAction.Defs
- Cited by
- 112 results in Mathlib
- Foundations
- Depth 13 from the axioms, rests on 77 definitions · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- AddSubmonoidproof · cited by 1,178
- AddActionstatement and proof · cited by 820
- AddAction.stabilizerAddSubmonoidproof · cited by 2
Cited by130
Results whose statement or proof uses this declaration.
- SubAddAction.ofStabilizerstatement and proof · cited by 29
- AddAction.mem_stabilizer_iffstatement · cited by 27
- IsAddQuotientCoveringMap.isCoveringMapproof · cited by 16
- AddAction.stabilizerEquivStabilizerstatement and proof · cited by 16
- SubAddAction.ofStabilizer.conjMapstatement · cited by 6
- AddAction.mem_stabilizer_setstatement · cited by 5
- AddAction.IsBlock.ncard_block_add_ncard_orbit_eqproof · cited by 4
- SubAddAction.ofStabilizer.snocstatement · cited by 4
- AddAction.ofQuotientStabilizerstatement and proof · cited by 4
- AddAction.stabilizer_coe_finsetstatement · cited by 4
- AddAction.index_stabilizerstatement · cited by 3
- SubAddAction.fixingAddSubgroupInsertEquivstatement and proof · cited by 3