Publication details

On the compositum of orthogonal cyclic fields of the same odd prime degree

Authors

GREITHER Cornelius Johannes KUČERA Radan

Year of publication 2020
Type Article in Periodical
Magazine / Source CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES
MU Faculty or unit

Faculty of Science

Citation
Doi http://dx.doi.org/10.4153/S0008414X20000589
Keywords Circular (cyclotomic) units; absolutely abelian fields; class groups
Description The aim of this paper is to study circular units in the compositum K of t cyclic extensions of Q (t ? 2) of the same odd prime degree l. If these fields are pairwise arithmetically orthogonal and the number s of primes ramifying in K/Q is larger than t, then a nontrivial root ? of the top generator ? of the group of circular units of K is constructed. This explicit unit ? is used to define an enlarged group of circular units of K, to show that l^{(s-t)l^{t-1}} divides the class number of K, and to prove an annihilation statement for the ideal class group of K.
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