Geodesic
Periodic groups saturated with finite simple groups $L_4(q)$
Algebra i logika, Tome 60 (2021) no. 6, pp. 549-556 Cet article a éte moissonné depuis la source Math-Net.Ru

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If $M$ is a set of finite groups, then a group $G$ is said to be saturated with the set $M$ (saturated with groups in $M$) if every finite subgroup of $G$ is contained in a subgroup isomorphic to some element of $M$. It is proved that a periodic group with locally finite centralizers of involutions, which is saturated with a set consisting of groups $L_4(q)$, where $q$ is odd, is isomorphic to $L_4(F)$ for a suitable field $F$ of odd characteristic.
Keywords: periodic group, locally finite group, involution
Mots-clés : saturation. 
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Wenbin Guo; D. V. Lytkina; V. D. Mazurov. Periodic groups saturated with finite simple groups $L_4(q)$. Algebra i logika, Tome 60 (2021) no. 6, pp. 549-556. http://geodesic.mathdoc.fr/item/AL_2021_60_6_a1/

[1] J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, R. A. Wilson, Atlas of finite groups, Clarendon Press, Oxford, 1985 | MR | Zbl

[2] P. Kleidman, M. Liebeck, The subgroup structure of the finite classical groups, London Math. Soc. Lect. Note Series, 129, Cambridge Univ. Press, Cambridge, 1990 | MR | Zbl

[3] J. N. Bray, D. F. Holt, C. M. Roney-Dougal, The maximal subgroups of the low-dimensional finite classical groups, London Math. Soc. Lecture Note Ser., 407, Cambridge Univ. Press, Cambridge, 2013 | MR | Zbl

[4] M. Suzuki, Group Theory II, Grundlehren Mathem. Wiss., 248, Springer-Verlag, New York etc., 1986 | DOI | MR | Zbl

[5] A. K. Shlepkin, A. G. Rubashkin, “O gruppakh, nasyschennykh konechnym mnozhestvom grupp”, Sib. matem. zh., 45:6 (2004), 1397–1400 | MR | Zbl

[6] A. V. Borovik, “Vlozheniya konechnykh grupp Shevalle i periodicheskie lineinye gruppy”, Sib. matem. zh., 24:6 (1983), 26–35 | MR | Zbl

[7] The GAP Group, GAP — Groups, Algorithms, Programming — A System for Computational Discrete Algebra, vers. 4.11.1, , 2021 https://www.gap-system.org