Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4594135 | Journal of Number Theory | 2014 | 16 Pages |
Abstract
Let k be a number field and Cl(k) its class group. Let Î be a finite group. Let Rt(k,Î) 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 Î. Let p be a prime number. In the present article, we suppose that Î=VâÏC, where V is an Fp-vector space of dimension r⩾2, C a cyclic group of order (prâ1)/(pâ1) with gcd(r,pâ1)=1, and Ï a faithful and irreducible Fp-representation of C in V. We prove that Rt(k,Î) is a subgroup of Cl(k) by means of an explicit description and properties of a p-ary cyclic Hamming code.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Maya Farhat, Bouchaïb Sodaïgui,