Theorems · Inductive type · group theory
AddSubgroup
(G : Type u_3) → [AddGroup G] → Type u_3
An additive subgroup of an additive group G is a subset containing 0, closed
under addition and additive inverse.
[Wikidata Q466109](https://www.wikidata.org/wiki/Q466109)
- Defined in
- Mathlib.Algebra.Group.Subgroup.Defs
- Cited by
- 3,232 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 2 definitions · uses no axioms
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement · cited by 4,410
Cited by3,759
Results whose statement or proof uses this declaration.
- MeasureTheory.Lpstatement · cited by 715
- AddSubgroup.zmultiplesstatement · cited by 493
- QuotientAddGroup.mkstatement and proof · cited by 348
- AddSubgroup.mapstatement and proof · cited by 189
- AddSubgroup.Normalstatement · cited by 183
- AddMonoidHom.kerstatement · cited by 158
- lpstatement · cited by 157
- AddSubgroup.closurestatement and proof · cited by 156
- AddMonoidHom.rangestatement · cited by 142
- selfAdjointstatement · cited by 135
- AddSubgroup.comapstatement and proof · cited by 123
- MeasureTheory.Lp.simpleFuncstatement · cited by 122
Showing the 200 most cited of 3,759.