Abstract
In this chapter we prove the theorem of Thaine, which was used in the previous chapter.
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Notes
- 1.
That is, \(\eta \equiv \alpha ^{q}\ \mathrm{mod}\,\ell\) for some \(\alpha \in \mathcal{O}_{K}\).
- 2.
A finite Galois extension of fields is called cyclic if its Galois group is cyclic.
References
Lang, S.: Algebra. Addison-Wesley, Reading (1965)
Thaine, F.: On the ideal class groups of real abelian number fields. Ann. Math. 128, 1–18 (1988)
Washington, L.: Introduction to Cyclotomic Fields, 2nd edn. Springer, New York (1997)
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Bilu, Y.F., Bugeaud, Y., Mignotte, M. (2014). The Theorem of Thaine. In: The Problem of Catalan. Springer, Cham. https://doi.org/10.1007/978-3-319-10094-4_12
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DOI: https://doi.org/10.1007/978-3-319-10094-4_12
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