top
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 or . 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.
P. V. Danchev. "Ulm-Kaplansky invariants of S(KG)/G." Bulletin of the Polish Academy of Sciences. Mathematics 53.2 (2005): 147-156. <http://eudml.org/doc/280900>.
@article{P2005, 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) = ℕ $ or $s_p(K) = ℕ ∪ 0$. 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.}, author = {P. V. Danchev}, journal = {Bulletin of the Polish Academy of Sciences. Mathematics}, language = {eng}, number = {2}, pages = {147-156}, title = {Ulm-Kaplansky invariants of S(KG)/G}, url = {http://eudml.org/doc/280900}, volume = {53}, year = {2005}, }
TY - JOUR AU - P. V. Danchev TI - Ulm-Kaplansky invariants of S(KG)/G JO - Bulletin of the Polish Academy of Sciences. Mathematics PY - 2005 VL - 53 IS - 2 SP - 147 EP - 156 AB - 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) = ℕ $ or $s_p(K) = ℕ ∪ 0$. 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. LA - eng UR - http://eudml.org/doc/280900 ER -