On the structure of a finitary linear group

O. Yu. Dashkova ; M. A. Salim ; O. A. Shpyrko

Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 23 (2017) no. 4, pp. 98-104

Résumé

Let $FL_{\nu}(K)$ be a finitary linear group of degree $\nu$ over a ring $K$, and let $K$ be an associative ring with the unit. We study periodic subgroups of $FL_{\nu}(K)$ in the cases when $K$ is an integral ring (Theorem $1$) and a commutative Noetherian ring (Theorem $2$). In both cases we prove that the periodic subgroups of $FL_{\nu}(K)$ are locally finite and describe their normal structure. In Theorem $3$ we describe the structure of finitely generated solvable subgroups of $FL_{\nu}(K)$ if $K$ is an integral ring, a commutative Noetherian ring, or an arbitrary commutative ring. We show that this structure is most complicated in the latter case.

Détail

Keywords: finitary linear group, commutative Noetherian ring, locally finite group.