Keyboard shortcuts

Press ← or → to navigate between chapters

Press ? to show this help

Press Esc to hide this help

Part IIUnitary Odd Central UProduct

Abstract

Actual part iiunitary odd central uproduct supplies the parameterized matrix, finite-field or ordered-product identities consumed by the whole-SU K5 width and intrinsic prescribed-product proof paths. All original hypotheses and actual carriers are retained; this source provides no oracle for bare automorphism recognition.

Theorem 1.1 (actual uniform odd Levi prescribed product).

Lean statement: D5/S3/FiniteGroups/NikolovSegal/Unitary/PartIIUnitaryOddCentralUProduct.actual_uniform_odd_Levi_prescribed_product

Proof. Machine-checked in Lean as D5/S3/FiniteGroups/NikolovSegal/Unitary/PartIIUnitaryOddCentralUProduct.actual_uniform_odd_Levi_prescribed_product (✓ std3). ∎

Source. Repository-derived.

Commentary.

Actual type-A PRODUCT on the central odd Levi. The entire prescribed D action is cancelled on ALL central elements; both scalar corrections and ONE ambient SU inner tuple precede all positive type-A targets.

Theorem 1.2 (actual uniform central odd U prescribed product).

Lean statement: D5/S3/FiniteGroups/NikolovSegal/Unitary/PartIIUnitaryOddCentralUProduct.actual_uniform_central_odd_U_prescribed_product

Proof. Machine-checked in Lean as D5/S3/FiniteGroups/NikolovSegal/Unitary/PartIIUnitaryOddCentralUProduct.actual_uniform_central_odd_U_prescribed_product (✓ std3). ∎

Source. Repository-derived.

Commentary.

The ENTIRE central odd positive unitary U, with arbitrary genuine prescribed D/Phi actions. Derived odd U=U2 P and both actual suppliers are consumed; ONE correction precedes ALL targets.

The results concern special-unitary matrix groups over finite fields. Their geometric setting is Nikolov and Segal, On finitely generated profinite groups, II: Products in quasisimple groups, Annals of Mathematics 165 (2007), 239-273, DOI 10.4007/annals.2007.165.239. Prescribed-product statements retain their field-size, rank and automorphism hypotheses.

References