Author:
Ao Lingfeng, ,Fei Shuanglin,Hong Shaofang
Abstract
<abstract><p>Let $ n\ge 8 $ be an integer and let $ p $ be a prime number satisfying $ \frac{n}{2} < p < n-2 $. In this paper, we prove that the Galois groups of the trinomials</p>
<p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ T_{n, p, k}(x): = x^n+n^kp^{(n-1-p)k}x^p+n^kp^{nk}, $\end{document} </tex-math></disp-formula></p>
<p><disp-formula> <label/> <tex-math id="FE2"> \begin{document}$ S_{n, p}(x): = x^n+p^{n(n-1-p)}n^px^p+n^pp^{n^2} $\end{document} </tex-math></disp-formula></p>
<p>and</p>
<p><disp-formula> <label/> <tex-math id="FE3"> \begin{document}$ E_{n, p}(x): = x^n+pnx^{n-p}+pn^2 $\end{document} </tex-math></disp-formula></p>
<p>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.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
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