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counter_unit_conjecture

Specification

The **Unit Conjecture** is false. At least there is a counterexample for any prime and zero characteristic: [Mu21] Murray, A. (2021). More Counterexamples to the Unit Conjecture for Group Rings. [Pa21] Passman, D. (2021). On the counterexamples to the unit conjecture for group rings. [Ga24] Gardam, G. (2024). Non-trivial units of complex group rings.

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Lean 4 Statement 
theorem counter_unit_conjecture :
    ∃ (G : Type) (_ : Group G) (_ : IsMulTorsionFree G),
    ∀ (p : ℕ) (_ : p = 0 ∨ p.Prime),
    ∃ (K : Type) (_ : Field K) (_ :  CharP K p) (u : (MonoidAlgebra K G)ˣ), ¬IsTrivialUnit u.val
ID: Wikipedia__Kaplansky__counter_unit_conjecture
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