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New ramification breaks and additive Galois structure

Nigel P. Byott, G. Griffith Elder (2005)

Journal de Théorie des Nombres de Bordeaux

Which invariants of a Galois p -extension of local number fields L / K (residue field of char p , and Galois group G ) determine the structure of the ideals in L as modules over the group ring p [ G ] , p the p -adic integers? We consider this question within the context of elementary abelian extensions, though we also briefly consider cyclic extensions. For elementary abelian groups G , we propose and study a new group (within the group ring 𝔽 q [ G ] where 𝔽 q is the residue field) and its resulting ramification filtrations....

Noncommutative independence in the infinite braid and symmetric group

Rolf Gohm, Claus Köstler (2011)

Banach Center Publications

This is an introductory paper about our recent merge of a noncommutative de Finetti type result with representations of the infinite braid and symmetric group which allows us to derive factorization properties from symmetries. We explain some of the main ideas of this approach and work out a constructive procedure to use in applications. Finally we illustrate the method by applying it to the theory of group characters.

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