Born in Veenendaal, Brinkhuis received his PhD in mathematics in 1981 at King's College London under supervisor of Albrecht Fröhlich with the thesis Embedding Problems and Galois Modules.
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Both of the above results are generalized by Leopoldt's "Spiegelungssatz", which relates the p-ranks of different isotypic components of the class group of a number field considered as a module over the Galois group of a Galois extension.