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

J 2021

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

GREITHER, Cornelius Johannes and Radan KUČERA

Basic information

Original name

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

Authors

GREITHER, Cornelius Johannes (276 Germany) and Radan KUČERA (203 Czech Republic, guarantor, belonging to the institution)

Edition

Canadian Journal of Mathematics-Journal canadien de mathématiques, Cambridge, Cambridge University Press, 2021, 0008-414X

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

United Kingdom of Great Britain and Northern Ireland

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

Impact factor

Impact factor: 1.455

RIV identification code

RIV/00216224:14310/21:00118788

Organization unit

Faculty of Science

DOI

http://dx.doi.org/10.4153/S0008414X20000589

UT WoS

000729499500004

Keywords in English

Circular (cyclotomic) units; absolutely abelian fields; class groups

Abstract

V originále

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.

Links

GA18-11473S, research and development project

Name: Grupy tříd ideálů abelovských rozšíření některých číselných těles

Investor: Czech Science Foundation

Citovat

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.

@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.

Detailed Information on Publication Record