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2018 On the relative Galois module structure of rings of integers in tame extensions
Adebisi Agboola, Leon R. McCulloh
Algebra Number Theory 12(8): 1823-1886 (2018). DOI: 10.2140/ant.2018.12.1823


Let F be a number field with ring of integers OF 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(OFG) of OFG that involves applying the work of McCulloh 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(OFG). 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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Adebisi Agboola. Leon R. McCulloh. "On the relative Galois module structure of rings of integers in tame extensions." Algebra Number Theory 12 (8) 1823 - 1886, 2018.


Received: 28 August 2015; Revised: 23 March 2018; Accepted: 2 July 2018; Published: 2018
First available in Project Euclid: 21 December 2018

zbMATH: 06999396
MathSciNet: MR3892966
Digital Object Identifier: 10.2140/ant.2018.12.1823

Primary: 11R33
Secondary: 11R32 , 11R65 , 19F99

Keywords: Galois module structure , inverse Galois problem , realisable classes , relative K-group , rings of integers

Rights: Copyright © 2018 Mathematical Sciences Publishers


Vol.12 • No. 8 • 2018
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