Geodesic
Characterization of Locally Finite Simple Groups of Type~$G_2$ over Fields of Odd Characteristics in the Class of Periodic Groups
Matematičeskie zametki, Tome 105 (2019) no. 4, pp. 519-525.

Voir la notice de l'article provenant de la source Math-Net.Ru

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
Mots-clés : saturation. 
@article{MZM_2019_105_4_a2,
     author = {X. Zhu and D. V. Lytkina and V. D. Mazurov},
     title = {Characterization of {Locally} {Finite} {Simple} {Groups} of {Type~}$G_2$ over {Fields} of {Odd} {Characteristics} in the {Class} of {Periodic} {Groups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {519--525},
     publisher = {mathdoc},
     volume = {105},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_105_4_a2/}
}
TY  - JOUR
AU  - X. Zhu
AU  - D. V. Lytkina
AU  - V. D. Mazurov
TI  - Characterization of Locally Finite Simple Groups of Type~$G_2$ over Fields of Odd Characteristics in the Class of Periodic Groups
JO  - Matematičeskie zametki
PY  - 2019
SP  - 519
EP  - 525
VL  - 105
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2019_105_4_a2/
LA  - ru
ID  - MZM_2019_105_4_a2
ER  - 
%0 Journal Article
%A X. Zhu
%A D. V. Lytkina
%A V. D. Mazurov
%T Characterization of Locally Finite Simple Groups of Type~$G_2$ over Fields of Odd Characteristics in the Class of Periodic Groups
%J Matematičeskie zametki
%D 2019
%P 519-525
%V 105
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2019_105_4_a2/
%G ru
%F MZM_2019_105_4_a2
X. Zhu; D. V. Lytkina; V. D. Mazurov. Characterization of Locally Finite Simple Groups of Type~$G_2$ over Fields of Odd Characteristics in the Class of Periodic Groups. Matematičeskie zametki, Tome 105 (2019) no. 4, pp. 519-525. http://geodesic.mathdoc.fr/item/MZM_2019_105_4_a2/

[1] R. W. Carter, Simple Groups of Lie Type, John Wiley Sons, London, 1972 | MR | Zbl

[2] V. V. Belyaev, “Lokalno konechnye gruppy Shevalle”, Issledovaniya po teorii grupp, UNTs AN SSSR, Sverdlovsk, 1984, 39–50

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

[4] B. Hartley, G. Shute, “Monomorphisms and direct limits of finite groups of Lie type”, Quart. J. Math. Oxford Ser. (2), 35:137 (1984), 49–71 | DOI | MR | Zbl

[5] S. Thomas, “The classification of the simple periodic linear groups”, Arch. Math. (Basel), 41:2 (1983), 103–116 | DOI | MR | Zbl

[6] M. J. Larsen, R. Pink, “Finite subgroups of algebraic groups”, J. Amer. Math. Soc., 24:4 (2011), 1105–1158 | DOI | MR | Zbl

[7] A. K. Shlepkin, “O nekotorykh periodicheskikh gruppakh, nasyschennykh konechnymi prostymi gruppami”, Matem. tr., 1:1 (1998), 129–138 | MR | Zbl

[8] A. G. Rubashkin, K. A. Filippov, “O periodicheskikh gruppakh, nasyschennykh gruppami $L_2(p^n)$”, Sib. matem. zhurn., 46:6 (2005), 1388–1392 | MR | Zbl

[9] D. V. Lytkina, A. A. Shlepkin, “Periodicheskie gruppy, nasyschennye konechnymi prostymi gruppami tipov $U_3$ i $L_3$”, Algebra i logika, 55:4 (2016), 441–448 | DOI | Zbl

[10] K. A. Filippov, Gruppy, nasyschennye konechnymi neabelevymi prostymi gruppami i ikh rasshireniyami, Dis. $\dots$ kand. fiz.-matem. nauk, Krasnoyarsk, 2005

[11] K. A. Filippov, “O periodicheskikh gruppakh, nasyschennykh konechnymi prostymi gruppami”, Sib. matem. zhurn., 53:2 (2012), 430–438 | MR | Zbl

[12] D. Gorenstein, Finite Groups, Chelsea Publ., New York, 1980 | MR | Zbl

[13] J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, R. A. Wilson, Atlas of Finite Groups. Maximal Subgroups and Ordinary Characters for Simple Group, Clarendon Press, Oxford, 1985 | MR

[14] D. Gorenstein, K. Harada, “Finite simple groups of low 2-rank and the families $G_2(q)$, $D^2_4(q)$, $q$ odd”, Bull. Amer. Math. Soc., 77:6 (1971), 829–862 | DOI | MR | Zbl

[15] 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