Corpus ID: 117781881

Principalization of $2$-class groups of type $(2,2,2)$ of biquadratic fields $\mathbb{Q}\left(\sqrt{\strut p_1p_2q},\sqrt{\strut -1}\right)$

@article{Azizi2014PrincipalizationO,
  title={Principalization of \$2\$-class groups of type \$(2,2,2)\$ of biquadratic fields \$\mathbb\{Q\}\left(\sqrt\{\strut p_1p_2q\},\sqrt\{\strut -1\}\right)\$},
  author={A. Azizi and A. Zekhnini and M. Taous and D. C. Mayer},
  journal={arXiv: Number Theory},
  year={2014}
}
  • A. Azizi, A. Zekhnini, +1 author D. C. Mayer
  • Published 2014
  • Mathematics
  • arXiv: Number Theory
  • Let $p_1\equiv p_2\equiv -q\equiv1 \pmod4$ be different primes such that $\displaystyle\left(\frac{2}{p_1}\right)= \displaystyle\left(\frac{2}{p_2}\right)=\displaystyle\left(\frac{p_1}{q}\right)=\displaystyle\left(\frac{p_2}{q}\right)=-1$. Put $d=p_1p_2q$ and $i=\sqrt{-1}$, then the bicyclic biquadratic field ${k}=\mathbb{Q}(\sqrt{d},i)$ has an elementary abelian $2$-class group, $\mathbf{C}l_2(k)$, of rank $3$. In this paper, we study the principalization of the $2$-classes of ${k}$ in its… CONTINUE READING
    3 Citations

    References

    SHOWING 1-10 OF 24 REFERENCES
    Sur une question de capitulation
    • 5
    • PDF
    A remark concerning Hilbert's Theorem 94.
    • 32
    On 2-class field towers of imaginary quadratic number fields
    • 7
    • PDF
    Algebraic Number Theory
    • 925
    Algebraic Number Theory, Second Edition
    • 51
    CLASSIFYING 2-GROUPS BY COCLASS
    • 38
    • PDF