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On the compositum of orthogonal cyclic fields of the same odd prime degree
- Source :
- Canadian Journal of Mathematics. 73:1506-1530
- Publication Year :
- 2020
- Publisher :
- Canadian Mathematical Society, 2020.
-
Abstract
- The aim of this paper is to study circular units in the compositum K of t cyclic extensions of ${\mathbb {Q}}$ ( $t\ge 2$ ) of the same odd prime degree $\ell $ . If these fields are pairwise arithmetically orthogonal and the number s of primes ramifying in $K/{\mathbb {Q}}$ is larger than $t,$ then a nontrivial root $\varepsilon $ of the top generator $\eta $ of the group of circular units of K is constructed. This explicit unit $\varepsilon $ is used to define an enlarged group of circular units of K, to show that $\ell ^{(s-t)\ell ^{t-1}}$ divides the class number of K, and to prove an annihilation statement for the ideal class group of K.
Details
- ISSN :
- 14964279 and 0008414X
- Volume :
- 73
- Database :
- OpenAIRE
- Journal :
- Canadian Journal of Mathematics
- Accession number :
- edsair.doi...........3d92c0320795bd021542cbfc1a5d1b96