Abstract
We show that for some recursive sequence \((c_m)_{m\ge 1}\) of integers and for sufficiently large n, the Galois group of polynomial \(f_n(x)=\frac{x^n}{n!}+c_{n-1}\frac{x^{n-1}}{(n-1)!}+\cdots + c_1\frac{x}{1!}+1\), contains the alternating group \(A_n\). In case n is a prime number, this group is the full symmetric group \(S_n\).
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Communicated by Rahim Zaare-Nahandi.
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Monsef-Shokri, K. On the Galois Groups of Some Recursive Polynomials. Bull. Iran. Math. Soc. 48, 1919–1926 (2022). https://doi.org/10.1007/s41980-021-00635-2
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DOI: https://doi.org/10.1007/s41980-021-00635-2