The 2-Class Group of Certain Families of Imaginary Triquadratic Fields

REFERENCES

[1] AZIZI, A.: Sur le 2-groupe de classes d’idaux de ℚ(d,i) , Rend. Circ. Mat. Palermo 48(2) (1999), 71–92.10.1007/BF02844380Search in Google Scholar

[2] AZIZI, A.: Units de certains corps de nombres imaginaires et abliens sur ℚ , Ann. Sci. Math. Qubec 23 (1999), 15–21.Search in Google Scholar

[3] AZIZI, A.—BENHAMZA, I.: Dtermination des corps K=ℚ(d,−2) dont les 2-groupes de classes sont de type (2, 2) (in French); [Determining fields K=ℚ(d,−2) whose class 2-groups are of type (2, 2)] Rend. Istit. Mat. Univ. Trieste 33 (2001), 83–104.Search in Google Scholar

[4] AZIZI, A.—BENHAMZA, I.: Sur la capitulation des 2-classes d’idaux de ℚ(d,−2) , Ann. Sci. Math. Qubec 29 (2005), 1–20.Search in Google Scholar

[5] AZIZI, A.—CHEMS-EDDIN, M. M.—ZEKHNINI, A.: On the rank of the 2-class group of some imaginary triquadratic number fields, Rend. Circ. Mat. Palermo (2) 70 (2021), 1751–1769.10.1007/s12215-020-00589-0Search in Google Scholar

[6] AZIZI, A.—MOUHIB, A.: Sur le rang du 2-groupe de classes de ℚ(m,d)∘m=2 ou un premier p ≡ 1 (mod 4), Trans. Amer. Math. Soc. 353 (2001), 2741–2752.10.1090/S0002-9947-01-02753-2Search in Google Scholar

[7] AZIZI, A.—MOUHIB, A.: Le 2-rang du groupe de classes de certains corps biquadratiques et applications, Internat. J. Math. 15 (2004), 169–182.10.1142/S0129167X04002235Search in Google Scholar

[8] AZIZI, A.—TAMIMI, M.—ZEKHNINI, A.: The 2-rank of the class group of some real cyclic quartic numberfields, Proc. Indian Acad. Sci. Math. Sci. 131 (2021), Art. No. 7.10.1007/s12044-020-00597-1Search in Google Scholar

[9] AZIZI, A.—TAMIMI, M.—ZEKHNINI, A.: The 2-rank of the class group of some real cyclic quartic numberfields II, Turkish J. Math. 45(3) (2021), 1241–1269.10.3906/mat-2011-46Search in Google Scholar

[10] BENJAMIN, E.—LEMMERMEYER, F.—SNYDER, C.: On the unit group of some multiquadratic number felds, Pacific J. Math. 230 (2007), 27–40.10.2140/pjm.2007.230.27Search in Google Scholar

[11] BROWN, E.—PARRY, C. J.: The 2-class group of certain biquadratic number fields, J. Reine Angew. Math. 295 (1977), 61–71.10.1515/crll.1977.295.61Search in Google Scholar

[12] BROWN, E.—PARRY, C. J.: The 2-class group of biquadratic number fields II, Pacific J. Math. 78 (1978), 11–26.10.2140/pjm.1978.78.11Search in Google Scholar

[13] CHEMS-EDDIN, M. M.—AZIZI, A.—ZEKHNINI, A.: Unit groups and Iwasawa lambda invariants of some multiquadratic number fields, Bol. Soc. Mat. Mex. 27 (2021), Art. No. 24.10.1007/s40590-021-00329-zSearch in Google Scholar

[14] CHEMS-EDDIN, M. M.—ZEKHNINI, A.—AZIZI, A.: Units and 2-class field towers of some multiquadratic number fields, Turk. J. Math. 44 (2020), 1466–1483.10.3906/mat-2003-117Search in Google Scholar

[15] CONNER, P. E.—HURRELBRINK, J.: Class Number Parity. Series in Pure Mathematics, vol. 8, World Scientific, Singapore, 1988.10.1142/0663Search in Google Scholar

[16] HERGLOTZ, G.: Uber einen Dirichletschen Satz, Math. Z. 12 (1922), 255–261.10.1007/BF01482079Search in Google Scholar

[17] KURODA, S.: Uber die Klassenzahlen algebraischer Zahlkorper, Nagoya Math. J. 1 (1950), 1–10.10.1017/S0027763000022777Search in Google Scholar

[18] KAPLAN, P.: Sur le 2-groupe de classes d’idaux des corps quadratiques, J. Reine Angew. Math. 283—284 (1976), 313–363.10.1515/crll.1976.283-284.313Search in Google Scholar

[19] KAPLAN, P.: Divisibility par 8 du nombre des classes des corps quadratiques dont le 2-groupe des classes est cyclique, et reciprocity biquadratique, J. Math. Soc. Japan 25 (1973), 596–608.10.2969/jmsj/02540596Search in Google Scholar

[20] KUCERA, R.: On the parity of the class number of a biquadratic field, J. Number Theory 52 (1995), 43–52.10.1006/jnth.1995.1054Search in Google Scholar

[21] LEMMERMEYER, F.: The ambiguous class number formula revisited, J. Ramanujan Math. Soc. 28 (2013), 415–421.Search in Google Scholar

[22] LEMMERMEYER, F.: Reciprocity Laws: From Euler to Eisenstein. Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2000.10.1007/978-3-662-12893-0Search in Google Scholar

[23] LEONARD P. A.—WILLIAMS, K. S.: On the divisibility of the class number of ℚ(−pq) by 16, Proc. Edinb. Math. Soc. (2) 26 (1983), 221–231.10.1017/S0013091500016928Search in Google Scholar

[24] McCALL, T. M.—PARRY, C. J.—RANALLI, R. R.: Imaginary bicyclic biquadratic fields with cyclic 2-class group, J. Number Theory 53 (1995), 88–99.10.1006/jnth.1995.1079Search in Google Scholar

[25] WADA, H.: On the class number and the unit group of certain algebraic number fields, J. Fac. Sci. Univ. Tokyo 13 (1966), 201–209.Search in Google Scholar