feat(GreensOpenProblems): 100 #1848
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This file introduces Green's Open Problem 100, discussing whether every group is well-approximated by finite groups and defining the concept of residual finiteness. closes: google-deepmind#1756
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Co-authored-by: Sachit Ramesh <sachit.rg17@gmail.com>
Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>
| Equivalently, is every group residually finite? A group $G$ is residually finite if for every | ||
| non-identity element $g \in G$, there exists a normal subgroup $N$ such that $G/N$ is finite | ||
| and $g \notin N$. |
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Where did you get this equivalence from? I can't find it in the PDF
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Are you using AI to avoid having to understand the conjecture yourself? Such behavior is wasting everyone's time and will get you banned from this repo.
| answer(sorry) ↔ | ||
| ∀ (G : Type) [Group G], | ||
| (∀ (g : G), g ≠ 1 → ∃ (N : Subgroup G), N.Normal ∧ Finite (G ⧸ N) ∧ g ∉ N) := by |
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This is certainly false. Consider G to be the rationals
I am using AI to help me understand the problem and write the code properly. |
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This file introduces Green's Open Problem 100, discussing whether every group is well-approximated by finite groups and defining the concept of residual finiteness.
closes: #1756
Reference: https://people.maths.ox.ac.uk/greenbj/papers/open-problems.pdf#problem.100