Geodesic
On the structure of a finitary linear group
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 23 (2017) no. 4, pp. 98-104 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: finitary linear group, commutative Noetherian ring, locally finite group. 
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O. Yu. Dashkova; M. A. Salim; O. A. Shpyrko. On the structure of a finitary linear group. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 23 (2017) no. 4, pp. 98-104. http://geodesic.mathdoc.fr/item/TIMM_2017_23_4_a9/

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