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Record W4394880856 · doi:10.26493/1855-3974.3087.f36

Z_3^8 is not a CI-group

2024· article· en· W4394880856 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueArs Mathematica Contemporanea · 2024
Typearticle
Languageen
FieldComputer Science
TopicDigital Image Processing Techniques
Canadian institutionsUniversity of Lethbridge
Fundersnot available
KeywordsMathematicsCombinatoricsGroup (periodic table)Chemistry

Abstract

fetched live from OpenAlex

A Cayley graph Cay(G, S) has the CI (Cayley Isomorphism) property if for every isomorphic graph Cay(G, T), there is a group automorphism α of G such that Sα = T. The DCI (Directed Cayley Isomorphism) property is defined analogously on digraphs. A group G is a CI-group if every Cayley graph on G has the CI property, and is a DCI-group if every Cayley digraph on G has the DCI property. Since a graph is a special type of digraph, this means that every DCI-group is a CI-group, and if a group is not a CI-group then it is not a DCI-group. In 2009, Spiga showed that ℤ38 is not a DCI-group, by producing a digraph that does not have the DCI property. He also showed that ℤ35 is a DCI-group (and therefore also a CI-group). Until recently the question of whether there are elementary abelian 3-groups that are not CI-groups remained open. In a recent preprint with Dave Witte Morris, we showed that ℤ310 is not a CI-group. In this paper we show that with slight modifications, the underlying undirected graph of order 38 described by Spiga is does not have the CI property, so ℤ38 is not a CI-group.

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.

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)0.001
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesScholarly communication, Insufficient payload (model declined to judge)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Methods · Consensus signal: none
Teacher disagreement score0.806
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0020.002
Open science0.0010.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.001

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.

Opus teacher head0.032
GPT teacher head0.283
Teacher spread0.251 · 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