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Periodic Groups Saturated with the Linear Groups of Degree 2 and the Unitary Groups of Degree 3 over Finite Fields of Odd Characteristic

Abstract

Let M denote the set of the simple 3-dimensional unitary groups U3 and the simple linear groups L2 over finite fields of odd characteristic.We prove that each periodic group saturated with groups in M is locally finite and isomorphic to either U3(Q) or L2(Q) for a suitable locally finite field Q of odd characteristic.

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Correspondence to D. V. Lytkina.

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Original Russian Text © D.V. Lytkina and A.A. Shlepkin, 2018, published in Matematicheskie Trudy, 2018, Vol. 21, No. 1, pp. 55–72.

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Lytkina, D.V., Shlepkin, A.A. Periodic Groups Saturated with the Linear Groups of Degree 2 and the Unitary Groups of Degree 3 over Finite Fields of Odd Characteristic. Sib. Adv. Math. 28, 175–186 (2018). https://doi.org/10.3103/S1055134418030033

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Keywords

  • group saturated with a set of groups
  • periodic group