×
Wei, X.; Guo, W.; Lytkina, D. V.; Mazurov, V. D.

Characterization of locally finite simple groups of the type \(^3D_4\) over fields of odd characteristic in the class of periodic groups. (English. Russian original) Zbl 1515.20188

Sib. Math. J. 59, No. 5, 799-804 (2018); translation from Sib. Mat. Zh. 59, No. 5, 1013-1019 (2018).
Summary: We prove that a periodic group is locally finite, given that each finite subgroup of the group lies in a subgroup isomorphic to a finite simple group of Lie type \(^3D_4\) over a field of odd characteristic.

Cited in 2 Documents

MSC:

20F50 Periodic groups; locally finite groups
20E32 Simple groups

Keywords:

periodic group; period; locally finite group; group of Lie type; group saturated with a set of groups
PDFBibTeX XMLCite
\textit{X. Wei} et al., Sib. Math. J. 59, No. 5, 799--804 (2018; Zbl 1515.20188); translation from Sib. Mat. Zh. 59, No. 5, 1013--1019 (2018)
Full Text: DOI

References:

[1] Carter R. W., Simple Groups of Lie Type, John Wiley and Sons, London (1972). · Zbl 0248.20015
[2] Belyaev, V. V., Locally finite Chevalley groups (1984) · Zbl 0587.20019
[3] Borovik A. V., “Embeddings of finite Chevalley groups and periodic linear groups,” Sib. Math. J., vol. 24, No. 6, 843-851 (1983). · Zbl 0551.20026
[4] Hartley B. and Shute G., “Monomorphisms and direct limits of finite groups of Lie type,” Q. J. Math. Oxford, Ser. 2, vol. 35, No. 137, 49-71 (1984). · Zbl 0547.20024
[5] Thomas S., “The classification of the simple periodic linear groups,” Arch. Math., vol. 41, 103-116 (1983). · Zbl 0518.20039
[6] Larsen M. J. and Pink R., “Finite subgroups of algebraic groups,” J. Amer. Math. Soc., vol. 24, No. 4, 1105-1158 (2011). · Zbl 1241.20054
[7] Shlepkin A. K., “On some periodic groups saturated by finite simple groups,” Mat. Tr., vol. 1, No. 1, 129-138 (1998). · Zbl 0905.20026
[8] Rubashkin A. G. and Filippov K. A., “Periodic groups saturated with the groups L2(pn),” Sib. Math. J., vol. 46, No. 6, 1119-1122 (2005).
[9] Lytkina D. V. and Shlepkin A. A., “Periodic groups saturated with finite simple groups of the types U3 and L3,” Algebra and Logic, vol. 55, No. 4, 441-448 (2016). · Zbl 1368.20043
[10] Filippov K. A., Groups Saturated with Finite Nonabelian Groups and Their Extensions [Russian], PhD Thesis, Krasnoyarsk (2005).
[11] Filippov K. A., “On periodic groups saturated by finite simple groups,” Sib. Math. J., vol. 53, No. 2, 345-351 (2012). · Zbl 1255.20037
[12] Isaacs I. M., Finite Group Theory, Amer. Math. Soc., Providence (2008) (Grad. Stud. Math.; vol. 92). · Zbl 1169.20001
[13] Conway J. H., Curtis R. T., Norton S. P., Parker R. A., and Wilson R. A., Atlas of Finite Groups. Maximal Subgroups and Ordinary Characters for Simple Groups, Clarendon Press, Oxford (1985). · Zbl 0568.20001
[14] Gorenstein D. and Harada K., “Finite simple groups of low 2-rank and the families G2(q), D2 4(q), q odd,” Bull. Amer. Math. Soc., vol. 77, No. 6, 829-862 (1971). · Zbl 0256.20014
[15] Bray J. N., Holt D. F., and Roney-Dougal C. M., The Maximal Subgroups of the Low-Dimensional Finite Classical Groups, Camb. Univ. Press, Cambridge (2013) (Lond. Math. Soc. Lect. Note Ser.). · Zbl 1303.20053
[16] Shunkov V. P., “On periodic groups with an almost regular involution,” Algebra and Logic, vol. 11, No. 4, 260-272 (1972). · Zbl 0275.20074
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.