The ℓ -rank of the real class group of cyclotomic fields

Gary Cornell; Michael I. Rosen

Compositio Mathematica (1984)

  • Volume: 53, Issue: 2, page 133-141
  • ISSN: 0010-437X

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Cornell, Gary, and Rosen, Michael I.. "The $\ell $-rank of the real class group of cyclotomic fields." Compositio Mathematica 53.2 (1984): 133-141. <http://eudml.org/doc/89679>.

@article{Cornell1984,
author = {Cornell, Gary, Rosen, Michael I.},
journal = {Compositio Mathematica},
keywords = {class number; maximal real subfield; cyclotomic field; cohomological approach; lower bounds for the -rank of the class group},
language = {eng},
number = {2},
pages = {133-141},
publisher = {Martinus Nijhoff Publishers},
title = {The $\ell $-rank of the real class group of cyclotomic fields},
url = {http://eudml.org/doc/89679},
volume = {53},
year = {1984},
}

TY - JOUR
AU - Cornell, Gary
AU - Rosen, Michael I.
TI - The $\ell $-rank of the real class group of cyclotomic fields
JO - Compositio Mathematica
PY - 1984
PB - Martinus Nijhoff Publishers
VL - 53
IS - 2
SP - 133
EP - 141
LA - eng
KW - class number; maximal real subfield; cyclotomic field; cohomological approach; lower bounds for the -rank of the class group
UR - http://eudml.org/doc/89679
ER -

References

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  1. [1] G. Cornell: Exponential growth of the l-rank of the class group of the maximal real subfield of cyclotomic fields (to appear). Zbl0519.12004MR682821
  2. [2] A. Fröhlich: On the absolute class group of abelian fields, J. of the London Math. Soc.29 (1954) 211-217. Zbl0055.03302MR66422
  3. [3] A. Fröhlich: On the absolute class group of abelian fields II, J. of the London Math. Soc.30 (1955) 72-80. Zbl0064.27305MR66424
  4. [4] Y. Furuta: On class field towers and the rank of ideal class groups, Nagoya Math. J.48 (1972) 147-157. Zbl0256.12009MR325574
  5. [5] D. Garbanati: Ivariants of the ideal class group and the Hasse norm theorem, J. Reine and Angew. Math.297 (1978) 159-171. Zbl0364.12008MR466072
  6. [6] F. Gerth: The Hasse Norm theorem for abelian extensions of number fields, Bulletin Amer. Math. Soc.83 (1977) 264-266. Zbl0348.12015MR422200
  7. [7] B. Huppert: Endliche Gruppen I. BerlinHeidelberg, New York: Springer-Verlag (1979). Zbl0412.20002MR224703
  8. [8] D. Kubert: The 2-divisibility of the class number of cyclotomic fields and the Stickelberger ideal (to appear). Zbl0584.12003MR850634
  9. [9] S. Lang: Units and class groups in number theory and algebraic geometry, Bullentin Amer. Math. Soc.6 (1982) 253-316. Zbl0482.12002MR648522
  10. [10] H.W. Leopoldt: Zur Geschlechtertheorie in abelschen Zahlkörpern, Math. Nach.9 (1953) 350-362. Zbl0053.35502MR56032
  11. [11] M. Razar: Central and genus class fields and the Hasse norm theorem, Comp. Math.35 (1977) 281-298. Zbl0376.12006MR466073
  12. [12] K. Yamazaki: On projective representations and ring extensions of finite groups, J. Fac. Sci. Univ. Tokyo10 (1964) 147-195. Zbl0125.01601MR180608

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