Theorems · Theorem · group theory
MulAction.isPretransitive_iff_base
∀ {G : Type u_1} {X : Type u_2} [inst : Group G] [inst_1 : MulAction G X] (a : X),
MulAction.IsPretransitive G X ↔ ∀ (x : X), ∃ g, g • a = xAn action of a group is pretransitive iff any element can be moved from a fixed given one.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- MulActionstatement and proof · cited by 1,294
- smul_smulproof · cited by 360
- MulAction.IsPretransitivestatement and proof · cited by 94
- inv_mul_cancel_rightproof · cited by 70
- MulAction.exists_smul_eqproof · cited by 32
Cited by4
Results whose statement or proof uses this declaration.
- SubMulAction.IsPretransitive.isPretransitive_ofFixingSubgroup_interproof · cited by 2
- MulAction.IsPreprimitive.of_isTrivialBlock_of_notMem_fixedPointsproof · cited by 1
- MulAction.IsPretransitive.of_partitionproof · cited by 1
- MulAction.isPretransitive_iff_orbit_eq_univproof · cited by 0