TY - JOUR

T1 - Galois groups of order 2n that contain a cyclic subgroup of order n

AU - Hwang, Y. S.

AU - Leep, David B.

AU - Wadsworth, Adrian R.

N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2003/12

Y1 - 2003/12

N2 - Let n be any integer with n > 1, and let F ⊆ L be fields such that [L:F] = 2, L is Galois over F, and L contains a primitive nth root of unity ζ. For a cyclic Galois extension M = L(α1/n) of L of degree n such that M is Galois over F, we determine, in terms of the action of Gal(L/F) on α and ζ, what group occurs as Gal(M/F). The general case reduces to that where n = pe, with p prime. For n = pe, we give an explicit parametrization of those α that lead to each possible group Gal(M/F).

AB - Let n be any integer with n > 1, and let F ⊆ L be fields such that [L:F] = 2, L is Galois over F, and L contains a primitive nth root of unity ζ. For a cyclic Galois extension M = L(α1/n) of L of degree n such that M is Galois over F, we determine, in terms of the action of Gal(L/F) on α and ζ, what group occurs as Gal(M/F). The general case reduces to that where n = pe, with p prime. For n = pe, we give an explicit parametrization of those α that lead to each possible group Gal(M/F).

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U2 - 10.2140/pjm.2003.212.297

DO - 10.2140/pjm.2003.212.297

M3 - Article

AN - SCOPUS:0942300501

SN - 0030-8730

VL - 212

SP - 297

EP - 319

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

IS - 2

ER -