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Record W2104269748 · doi:10.1142/9789812702616_0007

HYPERBOLIC GROUPS AND COMPLETELY SIMPLE SEMIGROUPS

2004· article· en· W2104269748 on OpenAlexaff
John Fountain, Mark Kambites

Bibliographic record

Venuenot available
Typearticle
Languageen
FieldMathematics
TopicGeometric and Algebraic Topology
Canadian institutionsCarleton University
Fundersnot available
KeywordsSimple (philosophy)Computer scienceAlgebra over a fieldMathematicsTheoretical computer sciencePure mathematicsEpistemology

Abstract

fetched live from OpenAlex

We begin with a brief introduction to the theory of word hyperbolic groups. We then consider four possible conditions which might reasonably be used as definitions or partial definitions of hyperbolicity in semigroups: having a hyperbolic Cayley graph; having hyperbolic Schützenberger graphs; having a context-free multipli-cation table; or having word hyperbolic maximal subgroups. Our main result is that these conditions coincide in the case of finitely generated completely simple semigroups. This paper is based on a lecture given at the workshop on Semigroups and Languages held at the Centro de Álgebra da Universidade de Lisboa in November 2002. The aim of the paper, as of the talk, is to provide semigroup theorists with a gentle introduction to the concept of a word hyperbolic group (hereafter referred to as simply a ‘hyperbolic group’), to discuss recent work of Gilman which makes it possible to introduce a notion of (word) hyperbolic semigroup and then to examine these ideas in the context of completely simple semigroups. The first three sections

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

How this classification was reachedexpand

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.013
Threshold uncertainty score0.464

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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.

Opus teacher head0.046
GPT teacher head0.293
Teacher spread0.246 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Classification

machine, unvalidated

Machine predicted; a candidate call from one teacher head, not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designTheoretical or conceptual
Domainnot available
GenreEmpirical

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".

Quick stats

Citations6
Published2004
Admission routes1
Has abstractyes

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