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In this paper, we investigate the 2-rank of the class group of some real cyclic quartic number fields. Precisely, we consider the case where the quadratic subfield is $$\mathbb {Q}(\sqrt{\ell })$$ Q ( ℓ ) with $$\ell \equiv 5(\mathrm{mod}\ 8)$$ ℓ ≡ 5 ( mod 8 ) is a prime.

The 2-rank of the class group of some real cyclic quartic number fields