Theorems · Theorem · group theory
IsPGroup.isMulCommutative_of_card_eq_prime_sq
∀ {p : ℕ} {G : Type u_1} [inst : Group G] [Fact (Nat.Prime p)], Nat.card G = p ^ 2 → IsMulCommutative GA group of order p ^ 2 is commutative. See also IsPGroup.commGroupOfCardEqPrimeSq
for the CommGroup instance.
- Defined in
- Mathlib.GroupTheory.PGroup
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
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- Groupstatement and proof · cited by 6,238
- Factstatement and proof · cited by 2,726
- HasQuotient.Quotientproof · cited by 2,301
- Nat.Primestatement and proof · cited by 2,059
- Nat.cardstatement and proof · cited by 844
- IsCyclicproof · cited by 122
- Subgroup.centerproof · cited by 121
- IsMulCommutativestatement · cited by 95
- isMulCommutative_of_isCyclic_quotient_center_selfproof · cited by 1
- IsPGroup.cyclic_center_quotient_of_card_eq_prime_sqproof · cited by 1
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