Realisable classes, Stickelberger subgroup and its behaviour under change of the base field

Siviero, Andrea

doi:10.5802/pmb.13

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The Stickelberger Pairing1

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2018

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“…it fails for the dihedral group D 2p of order 2p, where p > 3 is a prime. (See [30,Chapter 3] or [31] for an explicit description of the Stickelberger pairing in this case.) (b) Let χ 1 , .…”

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%