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arXiv · 2604.08642

A necessary condition for solvability by radicals

Askold Khovanskii
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Abstract

This note was prepared as a handout for the MAT401 course ``Polynomial equations and fields", taught at the University of Toronto in Spring 2026. It presents a proof of a necessary condition for the solvability of algebraic equations by radicals, based on Galois theory. We begin with a brief overview of the relevant basic results from Galois theory, as covered in MAT401, and use -- without proof -- several standard (and relatively simple) results from the course textbook [1]. The sufficient condition for solvability by radicals, which is based on linear algebra, we will present in the next handout.

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Askold Khovanskii. 2026-04-09. A necessary condition for solvability by radicals. https://arxiv.org/abs/2604.08642

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