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, +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
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