Ulm–Kaplansky invariants of
Volume 53 / 2005
Bulletin Polish Acad. Sci. Math. 53 (2005), 147-156
MSC: 16U60, 16S34, 20K10, 20K20.
DOI: 10.4064/ba53-2-4
Abstract
Let G be an infinite abelian p-group and let K be a field of the first kind with respect to p of characteristic different from p such that s_p(K) = {\mathbb N} or s_p(K)={\mathbb N}\cup\{0\}. The main result of the paper is the computation of the Ulm–Kaplansky functions of the factor group S(KG)/G of the normalized Sylow p-subgroup S(KG) in the group ring KG modulo G. We also characterize the basic subgroups of S(KG)/G by proving that they are isomorphic to S(KB)/B, where B is a basic subgroup of G.
