Theorems · Theorem · group theory
Subgroup.card_commutator_le_of_finite_commutatorSet
∀ (G : Type u_1) [inst : Group G] [Finite ↑(commutatorSet G)], Nat.card ↥(commutator G) ≤ Subgroup.cardCommutatorBound (Nat.card ↑(commutatorSet G))
A theorem of Schur: The size of the commutator subgroup is bounded in terms of the number of commutators.
- Defined in
- Mathlib.GroupTheory.Schreier
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
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- Set.Elemstatement and proof · cited by 7,166
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- LE.le.transproof · cited by 3,151
- Finitestatement and proof · cited by 3,029
- Nat.cardstatement and proof · cited by 844
- pow_succproof · cited by 374
- pow_posproof · cited by 292
- Subgroup.indexproof · cited by 150
- Dvd.dvd.transproof · cited by 148
- Subgroup.centerproof · cited by 121
- pow_dvd_powproof · cited by 56
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