On Characterization of Simple Orthogonal Groups of Odd Dimension in the Class of Periodic Groups

Abstract

Suppose that \( n \) is an integer, \( n\geq 3 \). We prove that a periodic group saturated with a set of the finite simple groups \( O_{2n+1}(q) \), where \( q \) is congruent to \( \pm 3 \) modulo 8, is isomorphic to \( O_{2n+1}(F) \) for some locally finite field \( F \).

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Funding

The work of D. V. Lytkina was supported by the Mathematical Center in Akademgorodok under Agreement No. 075–15–2019–1613 with the Ministry of Science and Higher Education of the Russian Federation; the work of V. D. Mazurov was supported by the Russian Science Foundation (Project 19–11–00039).

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Lytkina, D.V., Mazurov, V.D. On Characterization of Simple Orthogonal Groups of Odd Dimension in the Class of Periodic Groups. Sib Math J 62, 77–83 (2021). https://doi.org/10.1134/S0037446621010080

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Keywords

  • periodic group
  • group saturated with a set of groups
  • locally finite group

UDC

  • 512.542