The notation follows Mazur and Ullom, Galois module structure of units in real biquadratic number fields, Acta Arithmetica 111.2 (2004) [10.4064/aa111-2-1, MR:2039416]. There are four basic types, I-IV, which describe the structure of the units $U$ modulo roots of unity. The subtype describes the actual structure of the units. Type III means that there are fundamental units $e_1,e_2,e_3$ of the three quadratic subfields such that $\sqrt{e_1e_2},\sqrt{e_2e_3},\sqrt{e_3e_1}$ generate the rank 3 group $U/\{\pm 1\}$.

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- Last edited by David Roberts on 2019-05-03 17:28:55

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