Bibliographic record
Abstract
We discuss a number of problems in relatively hyperbolic groups.We show that the word problem and the conjugacy (search) problem are solvable in linear and quadratic time, respectively, for a relatively hyperbolic group, whenever the corresponding problem is solvable in linear and quadratic time in each parabolic subgroup.We also consider the class R of finitely generated toral relatively hyperbolic groups.We show that groups from R are commutative transitive and generalize a theorem proved by Baumslag in [Bau67] to R.Moreover, we discuss two definitions of (fully) residually-C groups, the classical Definition 1.2.1 and a modified Definition 1.2.5.Building upon results obtained by Ol'shanskii [Ol'93] and Osin [Osi10], we prove the equivalence of the two definitions for C = R.This is a generalization of the similar result obtained by Ol'shanskii for the class of torsion-free hyperbolic groups.Let Γ ∈ R be non-abelian and non-elementary.Kharlampovich and Miasnikov proved in [KM12] that a finitely generated fully residually-Γ group G embeds into an iterated extension of centralizers of Γ.We deduce from their theorem that every finitely generated fully residually-Γ group embeds into a group from R. On the other hand, we give an example of a finitely generated torsion-free fully residually-H group that does not embed into a group from R; H is the class of hyperbolic groups.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.002 | 0.009 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.008 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".