Bibliographic record
Abstract
Abstract Let ν and ω be two varieties of groups defined by the sets of laws V and W, respectively. We introduce the concept of a ω-ν-covering group of a given group and show that every two ω-ν-covering groups of a given group in ω are ν-isologic. Also, in the case ν ⊆ ω, we show the existence of such groups for a finite ν-perfect group in ω, and also that every automorphism of a finite ν-perfect group G in ω may be lifted to an automorphism of a ω-ν-covering group of G. Finally we show that if G is in ω ∩ ν, then all ω-ν-covering groups of G are Hopfian. Key Words: ω-ν-Covering groupν-Perfect groupBaer-invariantIsologismHopf property2000 Mathematics Subject Classification: 20E1020E3420E36 Acknowledgment We would like to express our sincere thanks and gratitude to Professors Robert G. Burns, Akbar Rhemtulla and Mazi Shirvani who read the manuscript and made valuable suggestions. This work was done while the first author visiting York University, and he would like to thank the hospitality of Mathematics and Statistics Department.
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How this classification was reachedexpand
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 | 0.001 | 0.003 |
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".