A Construction of the Groups of Units of Some Number Fields from Certain Subgroups
A Construction of the Groups of Units of Some Number Fields from Certain Subgroups
G=\langle\sigma, \tau\rangle$ ; $\sigma^{2n}=\tau^{2}=(\sigma\tau)^{2}=1$ .Let $K,$ $F$ and $\Omega$ be the invariant subfield of $\langle\tau\rangle,$ $\langle d\tau\rangle$ and $\langle\sigma^{n}\rangle$ respectively.The quadratic subfields $K_{2}$ and $F_{2}$ of $K$ and $F$ are the invariant subfields of $\langle\sigma^{2}, \tau\rangle$ and $\langle\sigma^{3}\tau, \sigma^{2}\rangle$ respectively.When $n=3$ , the cubic subfield $K_{3}=K\cap F$ is the invariant …