Abstract
Every locally finite group saturated by groups from the set of projective special linear groups of a fixed degree over finite fields is known to be isomorphic to the projective special linear group of the given fixed degree over a suitable locally finite field. We describe the locally finite groups saturated by groups from the set of full linear groups and special linear groups of a fixed degree over finite fields. These are either full linear groups or special linear groups of the given fixed degree over a suitable locally finite field.
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Funding
The author was supported by the Russian Science Foundation (Grant no. 19–71–10017-P)
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Translated from Sibirskii Matematicheskii Zhurnal, 2024, Vol. 65, No. 4, pp. 760–770. https://doi.org/10.33048/smzh.2024.65.413
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Shlepkin, A.A. On Locally Finite Groups Saturated by Full and Special Linear Groups over Finite Fields. Sib Math J 65, 869–877 (2024). https://doi.org/10.1134/S003744662404013X
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DOI: https://doi.org/10.1134/S003744662404013X