# Group theory > 14 AI-made results in group theory, each explained in plain English with its trust label, Lean status and sources. Canonical: https://closedform.nishachay.tech/science/mathematics/group-theory/ Last updated: 2026-10-14 14 results in OpenAI Math 2026. 14 AI-made results in group theory, from 22 papers in the OpenAI math collection, each explained in plain English. 12 have a formal Lean proof listed; 2 are claimed in a paper and not yet machine-checked. The oldest question here dates back to 1902: [An infinite finitely presented residually finite 2-group and a finitely presented nil algebra](https://closedform.nishachay.tech/e/openai-math-2026-247/). ## Results (14) - [Cannon's conjecture](https://closedform.nishachay.tech/e/openai-math-2026-246/) - Entry 246 · A hyperbolic group whose boundary is a sphere acts geometrically on hyperbolic three-space. (Formal proof listed) - [An infinite finitely presented residually finite 2-group and a finitely presented nil algebra](https://closedform.nishachay.tech/e/openai-math-2026-247/) - Entry 247 · Claims an infinite finitely presented group where every element has finite order, answering a Burnside question. (Formal proof listed) - [Thompson's group F is nonamenable](https://closedform.nishachay.tech/e/openai-math-2026-248/) - Entry 248 · Thompson's group F, a famous group of interval stretchings, is not amenable. (Formal proof listed) - [A finitely generated Eilenberg–Ganea counterexample](https://closedform.nishachay.tech/e/openai-math-2026-249/) - Entry 249 · Claims a group of cohomological dimension two with no two-dimensional classifying space, refuting Eilenberg–Ganea. (Formal proof listed) - [Boone–Higman embeddings with higher finiteness](https://closedform.nishachay.tech/e/openai-math-2026-250/) - Entry 250 · A group has a word-solving algorithm exactly when it sits inside a finitely presented simple group. (Formal proof listed) - [Amenability, unitarizability, and strong Ulam stability](https://closedform.nishachay.tech/e/openai-math-2026-251/) - Entry 251 · A discrete group is amenable exactly when every uniformly bounded representation can be made unitary. (Formal proof listed) - [A torsion-free hyperbolic group that is neither residually finite nor linear over any field](https://closedform.nishachay.tech/e/openai-math-2026-252/) - Entry 252 · A torsion-free hyperbolic group in which some element vanishes in every finite quotient. (Formal proof listed) - [An infinite finitely presented simple amenable group](https://closedform.nishachay.tech/e/openai-math-2026-253/) - Entry 253 · One infinite group that is simple, amenable and described by finitely many rules at once. (Formal proof listed) - [Classifying spaces and geometric obstructions for Artin groups](https://closedform.nishachay.tech/e/openai-math-2026-254/) - Entry 254 · Proves the Artin K(π,1) conjecture in finite rank, and finds an Artin group with no geometric CAT(0) action. (Formal proof listed) - [Quasi-isometric recognition of virtually polycyclic groups](https://closedform.nishachay.tech/e/openai-math-2026-255/) - Entry 255 · Any finitely generated group that looks like a virtually polycyclic group from far away is virtually polycyclic. (Formal proof listed) - [Nonsingular systems of equations over arbitrary groups](https://closedform.nishachay.tech/e/openai-math-2026-256/) - Entry 256 · Claims every nonsingular system of equations over any group is solvable in a larger group, settling Howie's conjecture. (Formal proof listed) - [A hyperbolic group without a geometric CAT(0) action](https://closedform.nishachay.tech/e/openai-math-2026-257/) - Entry 257 · A hyperbolic group that cannot act geometrically on any CAT(0) space, in any dimension. (Formal proof listed) - [Gersten’s conjecture and virtual compact specialness of one-relator groups](https://closedform.nishachay.tech/e/openai-math-2026-258/) - Entry 258 · Claims one-relator groups without Baumslag–Solitar subgroups are hyperbolic and virtually compact special. (Claimed, not checked) - [A group without fixed price](https://closedform.nishachay.tech/e/openai-math-2026-259/) - Entry 259 · Claims a finitely generated group with two free measure-preserving actions of different costs, so fixed price fails. 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