Boone–Higman embeddings with higher finiteness
What the paper claims, in its own words
A finitely generated group has decidable word problem exactly when it embeds in a finitely presented simple group, proving the Boone–Higman conjecture. The target can have type F∞: a classifying space with finitely many cells in each dimension. A single group of type F∞ can also contain every finitely presented group.
The plain-language explainer for this entry is still coming.
The original papers (3)
- Finite algebraic envelopes and the Boone–Higman conjecture (PDF, opens in a new tab) September 23, 2026
- Simple F∞ overgroups of groups with decidable word problem (PDF, opens in a new tab) September 23, 2026
- A universal group of type F∞ (PDF, opens in a new tab) September 23, 2026 Formal proof listed