Testing nilpotence of galois groups in polynomial time

Authors:
V. Arvind;Piyush P. Kurur
Affiliations:
Institute of Mathematical Sciences, Chennai, India;Indian Institute of Technology, Kanpur, India
Venue:
ACM Transactions on Algorithms (TALG)
Year:
2012

Citing 8
Cited 0

A compact representation for permutation groups

Journal of Algorithms
A course in computational algebraic number theory

A course in computational algebraic number theory
Computation of Galois groups over function fields

Mathematics of Computation
Efficient computation of minimal polynomials in algebraic extensions of finite fields

ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Galois group computation for rational polynomials

Journal of Symbolic Computation - Algorithmic methods in Galois Theory
Polynomial Time Algorithms for Galois Groups

EUROSAM '84 Proceedings of the International Symposium on Symbolic and Algebraic Computation
Factoring Polynomials over Algebraic Number Fields

SIAM Journal on Computing
A polynomial time nilpotence test for galois groups and related results

MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science

Quantified Score

Hi-index	0.00

Visualization

Abstract

We give the first polynomial-time algorithm for checking whether the Galois group Gal(f) of an input polynomial f(X) ∈ Q[X] is nilpotent: the running time of our algorithm is bounded by a polynomial in the size of the coefficients of f and the degree of f. Additionally, we give a deterministic polynomial-time algorithm that, when given as input a polynomial f(X) ∈ Q[X] with nilpotent Galois group, computes for each prime factor p of # Gal(f), a polynomial gp(X)∈ Q[X] whose Galois group of is the p-Sylow subgroup of Gal(f).