O.Yu. Dashkova, M.A. Salim, O.A. Shpyrko. On the structure of a finitary linear group ... P. 98-104

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.

The paper was received by the Editorial Office on September  20, 2017

Olga Yurievna Dashkova, Dr. Phys.-Math. Sci, Prof., the Branch of Moscow State University named
after M.V. Lomonosov in Sevastopol, 299001 Russia, e-mail: odashkova@yandex.ru .

Mohamed Ahmed Salim, Dr. Phys.-Math. Sci, Prof., United Arab Emirates University, Al-Ain,
15551 United Arab Emirates, e-mail: MSalim@uaeu.ac.ae .

Olga Alekseevna Shpyrko, Cand. Phys.-Math. Sci, Associate Prof., the Branch of Moscow State
University named after M.V. Lomonosov in Sevastopol, 299001 Russia, e-mail: shpyrko@mail.ru .

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