{"id":"palomar/PALOMAR-2026-11-05-000002","url":"https://github.com/32805433/Small-Groups/tree/4a302a9ce13b5aa39f1db413df511be39df4ef31","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-11-05-000002-v1.json","repo":"https://github.com/32805433/Small-Groups","tags":["math.GR","math.LO","msc:20F05","msc:20F10","msc:03D35"],"score":0,"title":"SmallGroups","trust":"high","domain":"math.GR","source":"palomar","authors":["Qiuyu Ren"],"reviews":0,"subject":"math.GR","summary":"Lean 4 proofs of four existence theorems: a two-generator, three-relator universal group with infinite cyclic abelianization and a displayed normal generator; an effective two-generator, four-relator family with undecidable triviality and universal nontrivial members; a torsion-free two-generator, four-relator group with undecidable word problem, infinite cyclic abelianization, and a displayed normal generator; and an effective two-generator, five-relator family with undecidable triviality whose members are all torsion-free.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-11-05","reactions":{},"formalized":true,"formalizes":[{"title":"small_presentations_and_unrecognizable_four_manifolds.tex","identifier":"","relationship":"formalizes"},{"title":"A universal group with thirteen relators","identifier":"https://hexagonmath.org/2610.00278","relationship":"adapts"},{"title":"The topology of discrete groups","identifier":"https://doi.org/10.1016/0022-4049(80)90040-7","relationship":"adapts"},{"title":"The homology of groups, profinite completions, and echoes of Gilbert Baumslag","identifier":"https://doi.org/10.1515/9783110638387-003","relationship":"adapts"},{"title":"Aspherical relative presentations","identifier":"https://doi.org/10.1017/S0013091500005290","relationship":"adapts"}]}