The kernel of the matrix [ij (modn)] when n is prime

Bueno, M.I.; Furtado, Susana; Karkoska, Jennifer; Mayfield, Kyanne; Samalis, Robert; Telatovich, Adam

doi:10.2140/involve.2016.9.265

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The Stickelberger Pairing1

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2018

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“…. , c d ) be the set of irreducible characters (respectively conjugacy classes) of G. We refer the reader to [5] for computations and conjectures concerning the rank of the d × d-matrix [ χ i , c j G ] associated to the Stickelberger pairing −, − G when G is cyclic.…”

Section: The Stickelberger Pairingmentioning

confidence: 99%

On the relative Galois module structure of rings of integers in tame extensions

Agboola

McCulloh

2018

Alg. Number Th.

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Let F be a number field with ring of integers O F and let G be a finite group.We describe an approach to the study of the set of realisable classes in the locally free class group Cl(O F G) of O F G that involves applying the work of the second-named author in the context of relative algebraic K theory. For a large class of soluble groups G, including all groups of odd order, we show (subject to certain mild conditions) that the set of realisable classes is a subgroup of Cl(O F G). This may be viewed as being a partial analogue in the setting of Galois module theory of a classical theorem of Shafarevich on the inverse Galois problem for soluble groups.

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Section: The Stickelberger Pairingmentioning

confidence: 99%