Theorems · Theorem · group theory
Matrix.card_GL_field
∀ {𝔽 : Type u_1} [inst : Field 𝔽] [inst_1 : Fintype 𝔽] (n : ℕ),
Nat.card (GL (Fin n) 𝔽) = ∏ i, (Fintype.card 𝔽 ^ n - Fintype.card 𝔽 ^ ↑i)The cardinal of the general linear group over a finite field.
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- Foundations
- Depth 128 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
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- Fintypestatement and proof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- Finset.univstatement and proof · cited by 3,473
- Finset.prodstatement and proof · cited by 2,356
- Fintype.cardstatement and proof · cited by 1,386
- Nat.cardstatement · cited by 844
- Matrix.GeneralLinearGroupstatement · cited by 556
- Fintype.card_finproof · cited by 270
- Nat.card_congrproof · cited by 133
- Module.finrank_fintype_fun_eq_cardproof · cited by 14
- Matrix.equiv_GL_linearindependentproof · cited by 1
- card_linearIndependentproof · cited by 1
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