Skip to Main content Skip to Navigation
Journal articles

On Steinitz classes of nonabelian Galois extensions and p-ary cyclic Hamming codes

Abstract : Let k be a number field and Cl(k) its class group. Let Γ be a finite group. Let Rt(k,Γ) be the subset of Cl(k) consisting of those classes which are realizable as Steinitz classes of tamely ramified Galois extensions of k with Galois group isomorphic to Γ. Let p be a prime number. In the present article, we suppose that Γ=V⋊ρC, where V is an Fp-vector space of dimension r⩾2, C a cyclic group of order (pr−1)/(p−1) with gcd(r,p−1)=1, and ρ a faithful and irreducible Fp-representation of C in V. We prove that Rt(k,Γ) is a subgroup of Cl(k) by means of an explicit description and properties of a p-ary cyclic Hamming code.
Document type :
Journal articles
Complete list of metadata

https://hal-uphf.archives-ouvertes.fr/hal-03149645
Contributor : Julie Cagniard Connect in order to contact the contributor
Submitted on : Tuesday, February 23, 2021 - 11:21:01 AM
Last modification on : Tuesday, October 19, 2021 - 6:38:16 PM

Links full text

Identifiers

Collections

Citation

Maya Farhat, Bouchaïb Sodaïgui. On Steinitz classes of nonabelian Galois extensions and p-ary cyclic Hamming codes. Journal of Number Theory, Elsevier, 2014, 134, pp.93-108. ⟨10.1016/j.jnt.2013.07.003⟩. ⟨hal-03149645⟩

Share

Metrics