Ulm–Kaplansky invariants of $S(KG)/G$

P. V. Danchev¹

¹ 13, General Kutuzov Street, block 7, floor 2, flat 4 4003 Plovdiv, Bulgaria

Bulletin of the Polish Academy of Sciences. Mathematics, Tome 53 (2005) no. 2, pp. 147-156.

Résumé

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 $G$.

Détail

DOI : 10.4064/ba53-2-4

Keywords: infinite abelian p group field first kind respect characteristic different mathbb mathbb cup main result paper computation ulm kaplansky functions factor group normalized sylow p subgroup group ring modulo characterize basic subgroups proving isomorphic where basic subgroup