On <i>s</i>-semipermutable or s-quasinormally Embedded Subgroups of Finite Groups
Bibliographic record
Abstract
Abstract Suppose that G is a finite group and H is a subgroup of G . H is said to be s -semipermutable in G if HG p = G p H for any Sylow p -subgroup Gp of G with ( p , | H |) = 1; H is said to be s -quasinormally embedded in G if for each prime p dividing the order of H , a Sylow p-subgroup of H is also a Sylow p-subgroup of some s -quasinormal subgroup of G . In every non-cyclic Sylow subgroup P of G we fix some subgroup D satisfying 1 < | D | < | P | and study the structure of G under the assumption that every subgroup H of P with | H | = | D | is either s-semipermutable or s -quasinormally embedded in G . Some recent results are generalized and unified.
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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 | 0.002 | 0.012 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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) | 0.037 | 0.010 |
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; both teacher heads agree on what is shown here.
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".