{"id":"palomar/PALOMAR-2026-08-31-000019","url":"https://github.com/Arthur742Ramos/MarshallHallTheorem/tree/449124d5b5659f0c34b5fbb46ffb671eeac4e08e","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-08-31-000019-v2.json","repo":"https://github.com/Arthur742Ramos/MarshallHallTheorem","tags":["math.GR","msc:20E07","msc:20F65","msc:05C25","group-theory","free-groups","lean-formalization"],"score":0,"title":"Marshall Hall's theorem through finite cores","trust":"high","domain":"math.GR","source":"palomar","authors":["Arthur Freitas Ramos","David Barros Hulak","Ruy J. G. B. de Queiroz"],"reviews":0,"subject":"math.GR","summary":"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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-01","reactions":{},"formalized":true,"formalizes":[{"title":"Subgroups of Finite Index in Free Groups","identifier":"10.4153/CJM-1949-017-2","relationship":"formalizes"},{"title":"On the Number of Generators of a Free Product","identifier":"10.1112/jlms/s1-18.1.12","relationship":"formalizes"}]}