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On the 2 -class group of some number fields with large degree

Mohamed Mahmoud Chems-Eddin, Abdelmalek Azizi, Abdelkader Zekhnini (2021)

Archivum Mathematicum

Let d be an odd square-free integer, m 3 any integer and L m , d : = ( ζ 2 m , d ) . In this paper, we shall determine all the fields L m , d having an odd class number. Furthermore, using the cyclotomic 2 -extensions of some number fields, we compute the rank of the 2 -class group of L m , d whenever the prime divisors of d are congruent to 3 or 5 ( mod 8 ) .

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