Resumen de On the 2-class field tower of \mathbb Q (\sqrt{2p_1p_2},i) and the Galois group of its second Hilbert 2-class field

Abdelmalek Azizi, Abdelkader Zekhnini, Mohammed Taous

• Let ?1 and ?2 be primes such that ?1≡?2≡5(mod8) , ?=−1‾‾‾√ , ?=2?1?2 , ?=ℚ(?‾‾√,?) , ?(1)2 be the Hilbert 2-class field of ? , ?(2)2 be the Hilbert 2-class field of ?(1)2 , ? be the Galois group of ?(2)2/? and ?(∗)=ℚ(?1‾‾√,?2‾‾√,2‾√,?) be the genus field of ? . The 2-part ??,2 of the class group of ? is of type (2,2,2) . Our goal is to study the 2-class field tower of ? and to calculate the order of ? .