Open Research Index

Howson's theorem through finite cores and Kurosh decomposition

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

Palomar Registrypalomar/PALOMAR-2026-09-01-000009Sep 1, 2026math.GRscore 0

Formalizes Howson's theorem for finite-rank free groups: the intersection of two finitely generated subgroups is finitely generated. The proof uses the repository's inclusion-compatible Marshall Hall construction to place one subgroup as a free factor of a finite-index overgroup, applies Schreier's finite-index theorem to the other subgroup, and then uses the actual Kurosh decomposition of the resulting subgroup of a binary free product. The final map from the relevant conjugate-intersection factor is defined from the factor inclusions and proved surjective onto the internal subgroup…

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