Maximality Degree Elements of Finite Cyclic Group Zpn, Zpmpn
Bibliographic record
Abstract
In this article, the concept of maximality degree of a finite group G, where G is cyclic group or is introduced and studied in details.The probability of a random subgroup of G to be maximal is measured by this quantity.For certain special kinds of finite groups, explicit formulas are obtained.We will give a value of one when the probability of , , and a value of zero when it does not maximal sub group.This will be useful in our research to calculate the degree of probability.Several limits of degrees of maximality are also calculated.We studied three cases, the first is when is a prime number in , the second is when is a prime number raised to a certain degree in , and the third case is when and are the product of two prime numbers, each of these prime numbers is raised to a certain degree in .We find an algorithm to compute the probability of maximality degree Pmax(G).We will use the CAP program to compute the number of maximal subgroups of group G.In this program, we will calculate the max sub groups when , is a large number that is difficult to calculate manually.
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.
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 | 0.000 |
| 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 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".