Periodica Mathematica Hungarica | 2021
Unit groups of some multiquadratic number fields and 2-class groups
Abstract
Let \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p\\equiv -q \\equiv 5\\pmod 8$$\\end{document}p≡-q≡5(mod8) be two prime integers. In this paper, we investigate the unit groups of the fields \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ L_1 =\\mathbb {Q}(\\sqrt{2}, \\sqrt{p}, \\sqrt{q}, \\sqrt{-1} )$$\\end{document}L1=Q(2,p,q,-1) and \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ L_1^+=\\mathbb {Q}(\\sqrt{2}, \\sqrt{p}, \\sqrt{q} )$$\\end{document}L1+=Q(2,p,q). Furthermore , we give the second 2-class groups of the subextensions of \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_1$$\\end{document}L1 as well as the 2-class groups of the fields \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ L_n =\\mathbb {Q}( \\sqrt{p}, \\sqrt{q}, \\zeta _{2^{n+2}} )$$\\end{document}Ln=Q(p,q,ζ2n+2) and their maximal real subfields.