Multiplicative groups of galois extensions

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Suppose that K is Galois over k with group G, and suppose that F1 … Fn are maximal among the intermediate subfields. Then it is shown that if G=Dp, p an odd prime, then K*/F1* … F*n is a subgroup of F*/k* · (F*)p where F is the unique proper Galois subfield. One then deduces that if G contains two dihedral groups Dp and Dq, p ≠ q and both odd, then K* = F*1 … F*n. These results are derived from calculations involving modules over the integral group ring Z[G].

Original languageEnglish (US)
Pages (from-to)122-137
Number of pages16
JournalJournal of Algebra
Issue number1
StatePublished - Apr 1 1994

ASJC Scopus subject areas

  • Algebra and Number Theory

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