Publication details
On the compositum of orthogonal cyclic fields of the same odd prime degree
| Authors | |
|---|---|
| Year of publication | 2021 |
| Type | Article in Periodical |
| Magazine / Source | Canadian Journal of Mathematics-Journal canadien de mathématiques |
| MU Faculty or unit | |
| Citation | |
| Web | https://www.cambridge.org/core/journals/canadian-journal-of-mathematics/article/abs/on-the-compositum-of-orthogonal-cyclic-fields-of-the-same-odd-prime-degree/1165F270D43F1AF619B6656FD07BEA54 |
| 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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