A Polynomial Time Nilpotence Test for Galois Groups and Related Results
V. Arvind, Piyush P Kurur

TL;DR
This paper presents a deterministic polynomial-time algorithm for testing if the Galois group of a polynomial is nilpotent, and generalizes solvability tests to determine if it belongs to certain group classes, with efficient computation of group order factors.
Contribution
It introduces a polynomial-time algorithm to determine nilpotence of Galois groups and extends solvability tests to broader group classes, including prime factorization of group order.
Findings
Polynomial-time nilpotence test for Galois groups
Generalization of Landau-Miller solvability test
Efficient computation of prime factors of Galois group order
Abstract
We give a deterministic polynomial-time algorithm to check whether the Galois group of an input polynomial is nilpotent: the running time is polynomial in . Also, we generalize the Landau-Miller solvability test to an algorithm that tests if is in : this algorithm runs in time polynomial in and and, moreover, if it computes all the prime factors of # \Gal{f}.
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Taxonomy
TopicsPolynomial and algebraic computation · Coding theory and cryptography · Cryptography and Residue Arithmetic
