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The Classification of the Finite Simple Groups: An Overview
- MONOGRAFÍAS DE LA REAL ACADEMIA DE CIENCIAS DE ZARAGOZA. 26: 89–104, (2004)
, 2004
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, 2008
"... In the process of computing the Galois group of a prime degree polynomial f(x) over Q we suggest a preliminary checking for the existence of non-real roots. If f(x) has non-real roots, then combining a 1871 result of Jordan and the classification of transitive groups of prime degree which follows fr ..."
Abstract
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In the process of computing the Galois group of a prime degree polynomial f(x) over Q we suggest a preliminary checking for the existence of non-real roots. If f(x) has non-real roots, then combining a 1871 result of Jordan and the classification of transitive groups of prime degree which follows from CFSG we get that the Galois group of f(x) contains Ap or is one of a short list. Let f(x) ∈ Q[x] be an irreducible polynomial of prime degree p ≥ 5 and r = 2s be the number of non-real roots of f(x). We show that if s satisfies s(s log s + 2log s + 3) ≤ p then Gal(f) = Ap, Sp. 1
