Abstract
Let G be a finite group of order g, and let m be a multiple of the orders of all the elements of G. Take as ground field K the field Q of rational numbers, and let Q(m) be the field obtained by adjoining the mth roots of unity to Q. The Galois group of Q(m) over Q is the group denoted Γ Q in 12.4; it is a subgroup of the group (Z/mZ)*. In fact:
Theorem (Gauss). We have Γ Q = (Z/mZ)*.
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© 1977 Springer-Verlag, New York Inc.
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Serre, JP. (1977). Rationality questions: examples. In: Linear Representations of Finite Groups. Graduate Texts in Mathematics, vol 42. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9458-7_13
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DOI: https://doi.org/10.1007/978-1-4684-9458-7_13
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