Unit groups and Iwasawa lambda invariants of some multiquadratic number fields

Abstract

Let $$q_1$$ q 1 and $$q_2$$ q 2 be two prime integers such that $$q_1\\equiv 7\\pmod 8$$ q 1 ≡ 7 ( mod 8 ) and $$q_2\\equiv 3\\pmod 8$$ q 2 ≡ 3 ( mod 8 ) . In this work we determine the unit groups of the fields $$\\mathbb {L}={\\mathbb {Q}}(\\sqrt{q_1}, \\sqrt{q_2}, \\sqrt{2},i)$$ L = Q ( q 1 , q 2 , 2 , i ) and $$\\mathbb {L}^+={\\mathbb {Q}}(\\sqrt{q_1}, \\sqrt{q_2}, \\sqrt{2})$$ L + = Q ( q 1 , q 2 , 2 ) . Furthermore, as applications we compute the Iwasawa $$\\lambda$$ λ -invariant for some multiquadratic number fields of the form $$F={\\mathbb {Q}}(\\sqrt{q_1}, \\sqrt{q_2},i)$$ F = Q ( q 1 , q 2 , i ) .