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Copyright Â© 2013 Association des Annales de l'Institut FourierGiven an algebraic number field k and a finite group Î\u93, we write â\u84\u9b(O k [Î\u93]) for the subset of the locally free classgroup Cl(O k [Î\u93]) consisting of the classes of rings of integers O N  in tame Galois extensions N/k with Gal(N/k)â\u89\u85Î\u93. We determine â\u84\u9b(O k [Î\u93]), and show it is a subgroup of Cl(O k [Î\u93]) by means of a description using a Stickelberger ideal and properties of some cyclic codes, when k contains a root of unity of prime order p and Î\u93=Vâ\u8b\u8aC, where V is an elementary abelian group of order p r  and C is a cyclic group of order m>1 acting faithfully on V and making V into an irreducible ð\u9d\u94½ p [C]-module. This extends and refines results of Byott, Greither and SodaÃ¯gui for p=2 in Crelle, respectively of Bruche and SodaÃ¯gui for p>2 in J. Number Theory, which cover only the case m=p r -1 and determine only the image â\u84\u9b(â\u84³) of â\u84\u9b(O k [Î\u93]) under extension of scalars from O k [Î\u93] to a maximal order â\u84³â\u8a\u83O k [Î\u93] in k[Î\u93]. The main result here thus generalizes the calculation of â\u84\u9b(O k [A 4 ]) for the alternating group A 4  of degree 4 (the case p=r=2) given by Byott and SodaÃ¯gui in Compositio

Realizable Galois module classes over the group ring for non abelian extensions