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Theorems · Theorem · group theory

faithfulSMul_iff

∀ {G : Type u_2} {α : Type u_3} [inst : Group G] [inst_1 : MulAction G α],
  FaithfulSMul G α ↔ ∀ (g : G), (∀ (a : α), g • a = a) → g = 1
Defined in
Mathlib.Algebra.Group.Action.Faithful
Cited by
1 results in Mathlib
Foundations
Depth 12 from the axioms · uses propext, Quot.sound
Assumes
GroupMulAction
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Set.powersetCard.faithfulSMul · cited by 1powersetCard.faithfulSMulGroup · cited by 6238Groupone_smul · cited by 1374one_smulMulAction · cited by 1294MulActioninv_inv · cited by 494inv_invFaithfulSMul · cited by 340FaithfulSMulSemigroupAction.mul_smul · cited by 291SemigroupAction.mul_smulFaithfulSMul.eq_of_smul_eq_smul · cited by 22FaithfulSMul.eq_of_smul_e…eq_inv_of_mul_eq_one_left · cited by 15eq_inv_of_mul_eq_one_leftfaithfulSMul_iffCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.