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

Y. S. Hwang, David B. Leep, Adrian R. Wadsworth

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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).

Original languageEnglish
Pages (from-to)297-319
Number of pages23
JournalPacific Journal of Mathematics
Volume212
Issue number2
DOIs
Publication statusPublished - 2003 Dec

ASJC Scopus subject areas

  • Mathematics(all)

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