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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2017, Volume 23, Number 4, Pages 98–104
DOI: https://doi.org/10.21538/0134-4889-2017-23-4-98-104
(Mi timm1470)
 

On the structure of a finitary linear group

O. Yu. Dashkovaa, M. A. Salimb, O. A. Shpyrkoa

a Branch of Moscow State University named after M.V. Lomonosov in Sevastopol, 299001 Russia
b United Arab Emirates University, Al-Ain, 15551 United Arab Emirates
References:
Abstract: 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.
Received: 20.09.2017
Bibliographic databases:
Document Type: Article
UDC: 512.544
MSC: 20F50
Language: Russian
Citation: O. Yu. Dashkova, M. A. Salim, O. A. Shpyrko, “On the structure of a finitary linear group”, Trudy Inst. Mat. i Mekh. UrO RAN, 23, no. 4, 2017, 98–104
Citation in format AMSBIB
\Bibitem{DasSalShp17}
\by O.~Yu.~Dashkova, M.~A.~Salim, O.~A.~Shpyrko
\paper On the structure of a finitary linear group
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2017
\vol 23
\issue 4
\pages 98--104
\mathnet{http://mi.mathnet.ru/timm1470}
\crossref{https://doi.org/10.21538/0134-4889-2017-23-4-98-104}
\elib{https://elibrary.ru/item.asp?id=30713963}
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