On the structure of the 2-Iwasawa module of some number fields of degree 16

Idriss Jerrari; Abdelmalek Azizi

Czechoslovak Mathematical Journal (2022)

  • Volume: 72, Issue: 4, page 1145-1156
  • ISSN: 0011-4642

Abstract

top
Let K be an imaginary cyclic quartic number field whose 2-class group is of type ( 2 , 2 , 2 ) , i.e., isomorphic to ℤ / 2 ℤ × ℤ / 2 ℤ × ℤ / 2 ℤ . The aim of this paper is to determine the structure of the Iwasawa module of the genus field K ( * ) of K .

How to cite

top

Jerrari, Idriss, and Azizi, Abdelmalek. "On the structure of the 2-Iwasawa module of some number fields of degree 16." Czechoslovak Mathematical Journal 72.4 (2022): 1145-1156. <http://eudml.org/doc/298923>.

@article{Jerrari2022,
abstract = {Let $K$ be an imaginary cyclic quartic number field whose 2-class group is of type $(2, 2, 2)$, i.e., isomorphic to $\mathbb \{Z\}/2\mathbb \{Z\}\times \mathbb \{Z\}/2\mathbb \{Z\}\times \mathbb \{Z\}/2\mathbb \{Z\}$. The aim of this paper is to determine the structure of the Iwasawa module of the genus field $K^\{(*)\}$ of $K$.},
author = {Jerrari, Idriss, Azizi, Abdelmalek},
journal = {Czechoslovak Mathematical Journal},
keywords = {cyclic quartic field; cyclotomic $\mathbb \{Z\}_2$-extension; 2-Iwasawa module; 2-class group; 2-rank},
language = {eng},
number = {4},
pages = {1145-1156},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the structure of the 2-Iwasawa module of some number fields of degree 16},
url = {http://eudml.org/doc/298923},
volume = {72},
year = {2022},
}

TY - JOUR
AU - Jerrari, Idriss
AU - Azizi, Abdelmalek
TI - On the structure of the 2-Iwasawa module of some number fields of degree 16
JO - Czechoslovak Mathematical Journal
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 72
IS - 4
SP - 1145
EP - 1156
AB - Let $K$ be an imaginary cyclic quartic number field whose 2-class group is of type $(2, 2, 2)$, i.e., isomorphic to $\mathbb {Z}/2\mathbb {Z}\times \mathbb {Z}/2\mathbb {Z}\times \mathbb {Z}/2\mathbb {Z}$. The aim of this paper is to determine the structure of the Iwasawa module of the genus field $K^{(*)}$ of $K$.
LA - eng
KW - cyclic quartic field; cyclotomic $\mathbb {Z}_2$-extension; 2-Iwasawa module; 2-class group; 2-rank
UR - http://eudml.org/doc/298923
ER -

References

top
  1. Azizi, A., Jerrari, I., Zekhnini, A., Talbi, M., 10.1016/j.jnt.2017.01.027, J. Number Theory 177 (2017), 562-588. (2017) Zbl1428.11190MR3629256DOI10.1016/j.jnt.2017.01.027
  2. Brown, E., Parry, C. J., 10.1515/crll.1977.295.61, J. Reine Angew. Math. 295 (1977), 61-71. (1977) Zbl0355.12007MR0457398DOI10.1515/crll.1977.295.61
  3. Chems-Eddin, M. M., The 2-Iwasawa module over certain octic elementary fields, Available at https://arxiv.org/abs/2007.05953 (2020), 4 pages. (2020) 
  4. Chems-Eddin, M. M., The rank of the 2-class group of some fields with large degree, Available at https://arxiv.org/abs/2001.00865 (2020), 9 pages. (2020) MR4414147
  5. Gras, G., 10.5802/aif.471, Ann. Inst. Fourier 23 (1973), 1-48 French. (1973) Zbl0276.12013MR360519DOI10.5802/aif.471
  6. Gras, G., 10.1007/978-3-662-11323-3, Springer Monographs in Mathematics. Springer, Berlin (2003). (2003) Zbl1019.11032MR1941965DOI10.1007/978-3-662-11323-3
  7. Greenberg, R., 10.2307/2373625, Am. J. Math. 98 (1976), 263-284. (1976) Zbl0334.12013MR0401702DOI10.2307/2373625
  8. Ishida, M., 10.1007/BFb0100829, Lecture Notes in Mathematics 555. Springer, Berlin (1976). (1976) Zbl0353.12001MR435028DOI10.1007/BFb0100829
  9. Kida, Y., 10.1016/0022-314X(82)90069-5, J. Number Theory 14 (1982), 340-352. (1982) Zbl0493.12015MR0660379DOI10.1016/0022-314X(82)90069-5
  10. Lemmermeyer, F., 10.1007/978-3-662-12893-0, Springer Monographs in Mathematics. Springer, Berlin (2000). (2000) Zbl0949.11002MR1761696DOI10.1007/978-3-662-12893-0
  11. Müller, K., 10.1017/S0305004118000026, Math. Proc. Camb. Philos. Soc. 166 (2019), 371-380. (2019) Zbl1462.11099MR3903123DOI10.1017/S0305004118000026
  12. Washington, L. C., 10.1007/978-1-4612-1934-7, Graduate Texts in Mathematics 83. Springer, New York (1997). (1997) Zbl0966.11047MR1421575DOI10.1007/978-1-4612-1934-7

NotesEmbed ?

top

You must be logged in to post comments.