Undecidability of group triviality with bounded presentation size
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Can triviality remain undecidable for finite group presentations with a fixed small number of generators and relators? The recorded target is an effective family with four generator slots and eleven relator slots.
Why it matters and what counts as progress
Why it matters: Smaller fixed presentation sizes sharpen how little syntactic complexity is needed for an undecidable group problem.
What counts as progress: Reduce the fixed presentation size in an undecidability construction or prove decidability under additional restrictions; a construction alone does not prove minimality.
How the problem developed
- 9 Sept 2026 · Construction [1]
Marc Kegel, Shana Yunsheng Li and Qiuyu Ren Constructed a three-generator, nine-relator group with unsolvable word problem as the starting point for fixed-size undecidable presentation families.
- 9 Sept 2026 · Undecidability result [1]
Marc Kegel, Shana Yunsheng Li and Qiuyu Ren Used the construction to give an effective family of four-generator, eleven-relator presentations with undecidable triviality; the counts are achieved bounds, not proven minima.
AI contributions 2
Small undecidable groups and fixed-size Adian–Rabin families
Kegel, Li and Ren give an effective family of finite presentations with two generators and ten relators for which deciding triviality is impossible. The count is an achieved presentation size, not a minimum.
Small undecidable groups and fixed-size Adian–Rabin families
Kegel, Li and Ren give an effective family of finite presentations with four generators and eleven relators for which deciding triviality is impossible. These are fixed presentation slots, not a minimality result.
Sources
Website timeline
Publication dates and editorial changes.
AI-developed two-generator family has undecidable triviality
AI-developed four-generator family has undecidable triviality