Mathlib Map

Theorems · Theorem · group theory

MulAction.period_dvd_orderOf

∀ {α : Type v} {M : Type u} [inst : Monoid M] [inst_1 : MulAction M α] (m : M) (a : α), MulAction.period m a ∣ orderOf m
Defined in
Mathlib.GroupTheory.GroupAction.Period
Cited by
2 results in Mathlib
Foundations
Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MonoidMulAction
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

MulAction.period_le_orderOf · cited by 0MulAction.period_le_order…MulAction.period_pos_of_orderOf_pos · cited by 0MulAction.period_pos_of_o…Monoid · cited by 3887Monoidone_smul · cited by 1374one_smulMulAction · cited by 1294MulActionorderOf · cited by 324orderOfpow_orderOf_eq_one · cited by 30pow_orderOf_eq_oneMulAction.period · cited by 26MulAction.periodMulAction.pow_smul_eq_iff_period_dvd · cited by 5MulAction.pow_smul_eq_iff…MulAction.period_dvd_orderOfCITED BYCITES

Cites7

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

Cited by2

Results whose statement or proof uses this declaration.