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Theorems · Theorem · group theory

MulAction.period_dvd_exponent

∀ {α : Type v} {M : Type u} [inst : Monoid M] [inst_1 : MulAction M α] (m : M) (a : α),
  MulAction.period m a ∣ Monoid.exponent 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
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Around this declaration

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

MulAction.period_le_exponent · cited by 1MulAction.period_le_expon…MulAction.period_pos_of_exponent_pos · cited by 0MulAction.period_pos_of_e…Monoid · cited by 3887Monoidone_smul · cited by 1374one_smulMulAction · cited by 1294MulActionMonoid.exponent · cited by 128Monoid.exponentMulAction.period · cited by 26MulAction.periodMonoid.pow_exponent_eq_one · cited by 13Monoid.pow_exponent_eq_oneMulAction.pow_smul_eq_iff_period_dvd · cited by 5MulAction.pow_smul_eq_iff…MulAction.period_dvd_exponentCITED BYCITES

Cites7

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Cited by2

Results whose statement or proof uses this declaration.