X. Zhu, D. V. Lytkina, V. D. Mazurov, “Characterization of Locally Finite Simple Groups of Type <nobr>$G_2$</nobr> over Fields of Odd Characteristics in the Class of Periodic Groups”, Mat. Zametki, 2019, Volume 105, Issue 4,Pages <nobr>519

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Characterization of Locally Finite Simple Groups of Type $G_2$ over Fields of Odd Characteristics in the Class of Periodic Groups

X. Zhu^a, D. V. Lytkina^b, V. D. Mazurov^c

^a Nanjing University of Aeronautics and Astronautics
^b Siberian State University of Telecommunications and Informatics, Novosibirsk
^c Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: We prove that a periodic group is locally finite, given that each of its finite subgroups lies in a subgroup isomorphic to a finite simple group $G_2$ of Lie type over a field of odd characteristic.

Keywords: periodic group, locally finite group, group of Lie type, saturation.

UDC: 512.542

Received: 15.01.2018
Revised: 20.04.2018

DOI: 10.4213/mzm11926