Why this work is in the frame
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Bibliographic record
Abstract
Let G be a group and G′ be its commutator subgroup. Denote by c(G) the minimal number such that every element of G′ can be expressed as a product of at most c(G) commutators. We find suitable bounds for c(G) when G is a free nilpotent by abelian group. Then we prove that c(G) is finite if G is a n-generator solvable group. And G has a nilpotent by abelian normal subgroup K of finite index. Moreover we have c(G) ≤ s(s + 1)/2 + 72n 2 + 47n, where s is the number of generators of K. We also prove that in a solvable group of finite Pruffer rank s every element of its commutator subgroup is equal to a product of at most s(s + 1)/2 + 72s 2 + 47s. And finally as a corollary of the above results we show that if A is a normal subgroup of a solvable group G such that G/A is a d-generator finite group. And A has finite Pruffer rank s. Then c(G) ≤ s(s + 1)/2 + 72(s 2 + n 2 ) + 47(s + n). The bounds we find are independent of the solvability length of the groups.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| 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