Finite Exceptional<i>p</i>-Groups of Small Order
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Bibliographic record
Abstract
Abstract A finite group is said to be exceptional if its minimal degree of a faithful permutation representation is strictly less than that of one of its factor groups, called a distinguished quotient. It was previously unknown if exceptional p-groups of order less than p 6 existed for p an odd prime. The author proved in his M.Sc thesis that there are none of order ≤p 4 and gave restrictions on the possible existence of distinguished quotients of exceptional groups of order p 5. In this article, an exceptional p-group of order p 5 is exhibited for p any odd prime. Key Words: Faithful representationFinite exceptional groupsMinimal degree p-groupsPermutation groupsAMS Subject Classification: 20B0520B35
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Full frame distilled prediction
Teacher imitationNot 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.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it