| Autor: |
Lingfeng Ao, Shuanglin Fei, Shaofang Hong |
| Jazyk: |
angličtina |
| Rok vydání: |
2022 |
| Předmět: |
|
| Zdroj: |
AIMS Mathematics, Vol 7, Iss 1, Pp 212-224 (2022) |
| Druh dokumentu: |
article |
| ISSN: |
2473-6988 |
| DOI: |
10.3934/math.2022013?viewType=HTML |
| Popis: |
Let $ n\ge 8 $ be an integer and let $ p $ be a prime number satisfying $ \frac{n}{2} < p < n-2 $. In this paper, we prove that the Galois groups of the trinomials $ T_{n, p, k}(x): = x^n+n^kp^{(n-1-p)k}x^p+n^kp^{nk}, $ $ S_{n, p}(x): = x^n+p^{n(n-1-p)}n^px^p+n^pp^{n^2} $ and $ E_{n, p}(x): = x^n+pnx^{n-p}+pn^2 $ are the full symmetric group $ S_n $ under several conditions. This extends the Cohen-Movahhedi-Salinier theorem on the irreducible trinomials $ f(x) = x^n+ax^s+b $ with integral coefficients. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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