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arXiv · 1708.06014

Galois groups of some iterated polynomials over cyclotomic extensions

Wade Hindes
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Abstract

Let $\varphi_p(z)=(z-1)^p+2-\zeta_p$, where $\zeta_p\in\bar{\mathbb{Q}}$ is a primitive $p$-th root of unity for some odd prime $p$. Building on previous work, we show that the $n$-th iterate $\varphi_p^n(z)$ has Galois group $[C_p]^n$, an iterated wreath product of cyclic groups, whenever $p$ is not a Wieferich prime.

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Wade Hindes. 2017-08-20. Galois groups of some iterated polynomials over cyclotomic extensions. https://arxiv.org/abs/1708.06014

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