Abstract
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).
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Danchev, P.V. Torsion Completeness of Sylow p-Groups in Semisimple Group Rings. Acta Math Sinica 20, 893–898 (2004). https://doi.org/10.1007/s10114-003-0304-0
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DOI: https://doi.org/10.1007/s10114-003-0304-0