Abstract
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 language | English (US) |
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Pages (from-to) | 122-137 |
Number of pages | 16 |
Journal | Journal of Algebra |
Volume | 165 |
Issue number | 1 |
DOIs | |
State | Published - Apr 1 1994 |
ASJC Scopus subject areas
- Algebra and Number Theory