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Class Group Relations from Burnside Ring Idempotents

✍ Scribed by Robert Boltje

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 337 KB
Volume: 66
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1997.2165

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✦ Synopsis

We show that for each finite cohomological Mackey functor on a finite group G there exist explicit relations in the category of finite abelian groups between the evaluations of the Mackey functor at all the subgroups, one for each conjugacy class of nonhypo-elementary subgroups of G. Furthermore, we show that the class groups of the intermediate fields of a Galois extension of number fields form such a Mackey functor on the Galois group, thereby obtaining class group relations by using the presence of the structure of a cohomological Mackey functor.

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