Geodesic
Finite almost simple groups whose Gruenberg–Kegel graphs as abstract graphs are isomorphic to subgraphs of the Gruenberg–Kegel graph of the alternating group $A_{10}$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1378-1382 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the problem of describing finite groups whose the Gruenberg-Kegel graphs as abstract graphs are isomorphic to the Gruenberg–Kegel graph of the alternating group $A_{10}$. In the given paper, we prove that if such group is non-solvable then its quotient group by solvable radical is almost simple and classify all finite almost simple groups whose the Gruenberg-Kegel graphs as abstract graphs are isomorphic to subgraphs of the Gruenberg–Kegel graph of $A_{10}$.
Keywords: finite group, almost simple group, 4-primary group, Gruenberg–Kegel graph. 
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     author = {A. S. Kondrat'ev and N. A. Minigulov},
     title = {Finite almost simple groups whose {Gruenberg{\textendash}Kegel} graphs as abstract graphs are isomorphic to subgraphs of the {Gruenberg{\textendash}Kegel} graph of the alternating group $A_{10}$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
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A. S. Kondrat'ev; N. A. Minigulov. Finite almost simple groups whose Gruenberg–Kegel graphs as abstract graphs are isomorphic to subgraphs of the Gruenberg–Kegel graph of the alternating group $A_{10}$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1378-1382. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a28/

[1] Y. Bugeaud, Z. Cao, M. Mignotte, “On simple $K_4$-groups”, J. Algebra, 241:10 (2001), 658–668 | DOI | MR | Zbl

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

[3] D. Gorenstein, Finite groups, Harper and Row, New York–London, 1968 | MR | Zbl

[4] D. Gorenstein, R. Lyons, R. Solomon, The classification of the finite simple groups. Number 3, Mathematical Surveys and Monographs, 40, no. 3, 1998 | MR

[5] M. Herzog, “On finite simple groups of order divisible by three primes only”, J. Algebra, 10:3 (1968), 383–388 | DOI | MR | Zbl

[6] B. Huppert, W. Lempken, “Simple groups of order divisible by at most four primes”, Proc. F. Scorina Gomel State University, Problems in algebra, 16:3 (2000), 64–75 | MR | Zbl

[7] A.S. Kondrat'ev, “Finite groups with prime graph as in the group $Aut(J_2)$”, Proc. Steklov Inst. Math., 283:1 (2013), S78–S85 | MR | Zbl

[8] A.S. Kondrat'ev, “Finite groups that have the same prime graph as the group $A_{10}$”, Proc. Steklov Inst. Math., 285:1, Suppl. 1 (2014), S99–S107 | MR | Zbl

[9] A.S. Kondrat'ev, I.V. Khramtsov, “On finite triprimary groups”, Trudy Inst. Mat. Mech. UrO RAN, 16, no. 3, 2010, 150–158

[10] A.S. Kondrat'ev, I.V. Khramtsov, “On finite tetraprimary groups”, Proc. Steklov Inst. Math., 279, Suppl. 1 (2012), 43–61 | DOI | Zbl

[11] W.J. Shi, “On simple $K_4$-groups”, Chinese Scince Bull., 36:17 (1991), 1281–1283