Galois Groups of CM Fields of Degrees 12, 16, 18, 20 and 24

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Galois Groups of CM Fields of Degrees 12, 16, 18, 20 and 24 is written by Nicholas C. Zoller and published by . It's available with International Standard Book Number or ISBN identification 1109389949 (ISBN 10) and 9781109389944 (ISBN 13).

We also study the ranks of CM types. Nondegenerate CM types have rank n + 1 and make up the majority of CM types for a given CM field. In contrast, degenerate CM types have rank less than n + 1 and occur less frequently. Dodson was concerned with the identification of degenerate CM types and their relationship with CM fields that contain an imaginary quadratic subfield. We extend this investigation from n = 6 to n = 8, 9, 10, and 12. Specifically, when n = 6, we show that every degenerate CM type occurs as an orbit of types of size at least 2n = 12 and that every degenerate CM type arises from a CM field that contains an imaginary quadratic subfield. When n = 9, we show that every degenerate CM type arises from a CM field that contains an imaginary quadratic subfield. We also show that the orbits of rank 6 all have size 12