Open Research Index

Grushko--Neumann rank additivity for free products

Arthur Freitas Ramos, David Barros Hulak, Ruy J. G. B. de Queiroz

Palomar Registrypalomar/PALOMAR-2026-09-01-000013Sep 1, 2026math.GRscore 0

Formalizes the binary Grushko--Neumann theorem: the minimal number of generators of a free product of two finitely generated groups is the sum of the minimal numbers of generators of the factors. The central theorem is proved by a kernel-checked finite labelled-graph reduction. For a minimal null path, the implemented reduction uniformly performs a source unfold, a subsequent safe fold, and an explicit monochromatic-vertex contraction; this gives the strict decrease used by strong induction and the separated-generator lower bound. The repository also retains the finite-core and free-group…

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