Open Research Index

Marshall Hall's theorem through finite cores

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

Palomar Registrypalomar/PALOMAR-2026-08-31-000019Sep 1, 2026math.GRscore 0

Formalizes Marshall Hall's finite-index free-factor theorem for finitely generated subgroups of finite-rank free groups. The proof extracts the finitely many suffix states of a subgroup generating set, completes the resulting partial generator actions to permutations of a finite state set, identifies the connected orbit with a finite core, and extends a geodesic spanning tree to obtain an inclusion-compatible free-product decomposition. The repository also proves binary and finite-indexed free-group instances of Grushko--Neumann rank additivity, the arbitrary-factor binary theorem, and the…

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