Theorems · Theorem · group theory
Module.stabilizer_units_eq_bot_of_ne_zero
∀ (R : Type u_1) {M : Type u_2} [inst : Ring R] [IsDomain R] [inst_2 : AddCommGroup M] [inst_3 : Module R M]
[Module.IsTorsionFree R M] {x : M}, x ≠ 0 → MulAction.stabilizer Rˣ x = ⊥- Defined in
- Mathlib.GroupTheory.GroupAction.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- Bot.botstatement · cited by 4,720
- Subgroupstatement · cited by 3,593
- Unitsstatement and proof · cited by 2,804
- IsDomainstatement and proof · cited by 2,196
- Units.valproof · cited by 1,966
- one_smulproof · cited by 1,374
- sub_selfproof · cited by 996
- Module.IsTorsionFreestatement and proof · cited by 600
- sub_eq_zeroproof · cited by 407
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