Open Research Index

Existence of a Model Companion for Groups of Exponent 3: Lean Formalization

Yawara Ishida

Palomar Registrypalomar/PALOMAR-2026-09-26-000004Sep 26, 2026math.LOscore 0

This project formalizes the existence of a model companion for the first-order theory of groups satisfying x^3 = 1. Its principal group-theoretic result gives a uniform, explicit bound on the number of generators needed to witness a failure of amalgamation with an existentially closed exponent-three group. The development follows the accompanying manuscript through free groups, associated graded Lie algebras, strict extensions, and the bounded-amalgamation criterion.

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