Theorems · Theorem · group theory
Matrix.SpecialLinearGroup.toGL_mem_center_iff
∀ {n : Type u_1} {R : Type u_2} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : CommRing R]
(g : Matrix.SpecialLinearGroup n R),
Matrix.SpecialLinearGroup.toGL g ∈ Subgroup.center (GL n R) ↔ g ∈ Subgroup.center (Matrix.SpecialLinearGroup n R)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableEqCommRing
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Cites36
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- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Fintypestatement and proof · cited by 7,736
- Matrixstatement · cited by 4,303
- MonoidHomstatement · cited by 3,629
- Subgroupstatement · cited by 3,593
- Finset.univproof · cited by 3,473
- Unitsproof · cited by 2,804
- Finset.prodproof · cited by 2,356
- Units.valproof · cited by 1,966
- Fintype.cardproof · cited by 1,386
- IsEmptyproof · cited by 759
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