| GREITHER, Cornelius Johannes a 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, roč. 73, č. 6, s. 1506-1530. ISSN 0008-414X. Dostupné z: 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 a 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, roč.~73, č.~6, s.~1506-1530. ISSN~0008-414X. Dostupné z: https://dx.doi.org/10.4153/S0008414X20000589.
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