Let G be an abelian p-group and K be a field of the first kind with respect to p of charK p and of s_p(K)=N or N∪{0}.Then it is shown that the normed Sylow p-subgroup S(KG)is torsion complete if and only if G is boun...Let G be an abelian p-group and K be a field of the first kind with respect to p of charK p and of s_p(K)=N or N∪{0}.Then it is shown that the normed Sylow p-subgroup S(KG)is torsion complete if and only if G is bounded(Theorem 1).An analogous fact is proved for the case when K is of the second kind(Theorem 2).These completely settle a conjecture posed by us in Compt.Rend. Acad.Bulg.Sci.(1993)and are also a supplement to our result in the modular case published in Acta Math.Hungar.(1997).展开更多
文摘Let G be an abelian p-group and K be a field of the first kind with respect to p of charK p and of s_p(K)=N or N∪{0}.Then it is shown that the normed Sylow p-subgroup S(KG)is torsion complete if and only if G is bounded(Theorem 1).An analogous fact is proved for the case when K is of the second kind(Theorem 2).These completely settle a conjecture posed by us in Compt.Rend. Acad.Bulg.Sci.(1993)and are also a supplement to our result in the modular case published in Acta Math.Hungar.(1997).
