GREITHER, Cornelius Johannes and Radan KUČERA. On the compositum of orthogonal cyclic fields of the same odd prime degree. Canadian Journal of Mathematics-Journal canadien de mathématiques. Cambridge: Cambridge University Press, 2021, vol. 73, No 6, p. 1506-1530. ISSN 0008-414X. Available from: https://dx.doi.org/10.4153/S0008414X20000589. |
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@article{1703996, author = {Greither, Cornelius Johannes and Kučera, Radan}, article_location = {Cambridge}, article_number = {6}, doi = {http://dx.doi.org/10.4153/S0008414X20000589}, keywords = {Circular (cyclotomic) units; absolutely abelian fields; class groups}, language = {eng}, issn = {0008-414X}, journal = {Canadian Journal of Mathematics-Journal canadien de mathématiques}, title = {On the compositum of orthogonal cyclic fields of the same odd prime degree}, url = {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}, volume = {73}, year = {2021} }
TY - JOUR ID - 1703996 AU - Greither, Cornelius Johannes - Kučera, Radan PY - 2021 TI - On the compositum of orthogonal cyclic fields of the same odd prime degree JF - Canadian Journal of Mathematics-Journal canadien de mathématiques VL - 73 IS - 6 SP - 1506-1530 EP - 1506-1530 PB - Cambridge University Press SN - 0008414X KW - Circular (cyclotomic) units KW - absolutely abelian fields KW - class groups UR - 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 N2 - 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 ε of the top generator η of the group of circular units of K is constructed. This explicit unit ε 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. ER -
GREITHER, Cornelius Johannes and Radan KUČERA. On the compositum of orthogonal cyclic fields of the same odd prime degree. \textit{Canadian Journal of Mathematics-Journal canadien de mathématiques}. Cambridge: Cambridge University Press, 2021, vol.~73, No~6, p.~1506-1530. ISSN~0008-414X. Available from: https://dx.doi.org/10.4153/S0008414X20000589.
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