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J. S. Williams, “Prime graph components of finite groups,” J. Alg., 69, No. 2, 487–513 (1981).
A. S. Kondratiev, “Prime graph components of finite simple groups,” Mat. Sb., 180, No. 6, 787–797 (1989).
N. Iiyori and H. Yamaki, “Prime graph components of the simple groups of Lie type over the field of even characteristic,” J. Alg., 155, No. 2, 335–343 (1993).
N. Iiyori and H. Yamaki, “Corrigendum to: Prime graph components of the simple groups of Lie type over the field of even characteristic,” J. Alg., 181, No. 2, 659 (1996).
M. S. Lucido, “Prime graph components of finite almost simple groups,” Rend. Semin. Mat. Univ. Padova, 102, 1–22 (1999).
M. S. Lucido, Addendum to “Prime graph components of finite almost simple groups,” Rend. Semin. Mat. Univ. Padova, 107, 189–190 (2002).
A. V. Vasiliev and E. P. Vdovin, “An adjacency criterion for the prime graph of a finite simple group,” Algebra and Logic, 44, No. 6, 381–406 (2005).
A. V. Vasiliev and E. P. Vdovin, “Cocliques of maximal size in the prime graph of a finite simple group,” Algebra and Logic, 50, No. 4, 291–322 (2011).
A. S. Kondrat’ev and I. V. Khramtsov, “Finite 3-primary groups,” Trudy Inst. Mat. Mekh. UrO RAN, 16, No. 3, 150–158 (2010).
A. S. Kondrat’ev and I. V. Khramtsov, “Finite 4-primary groups,” Trudy Inst. Mat. Mekh. UrO RAN, 17, No. 4, 142–159 (2011).
A. S. Kondrat’ev and I. V. Khramtsov, “Finite nonsimple 3-primary groups,” Sib. El. Mat. Izv., 9, 472–477 (2012); http://semr.math.nsc.ru/v9/p472-477.pdf.
A. S. Kondrat’ev and I. V. Khramtsov, “Complete reducibility of some GF(2)A 7-modules,” Trudy Inst. Mat. Mekh. UrO RAN, 18, No. 3, 139–143 (2012).
I. V. Khramtsov, “Finite nonsimple 4-primary groups,” Sib. El. Mat. Izv., 11, 695–708 (2014); http://semr.math.nsc.ru/v11/p695-708.pdf.
A. S. Kondrat’ev and I. V. Khramtsov, “Finite graphs with disconnected prime graph and composition factor isomorphic to L 3(17),” Proc. Int. Conf. “Algebra and Mathematical Logic: Theory and Applications,” Kazan State Univ., Kazan (2014), pp. 81/82.
A. S. Kondrat’ev, I. D. Suprunenko, and I. V. Khramtsov, “Modular representations of the group L 3(17),” Proc. Int. Conf. “Mal’tsev Readings,” Institute of Mathematics, Novosibirsk State University, Novosibirsk (2014), p. 63.
A. S. Kondrat’ev and I. V. Khramtsov, “Finite graphs with disconnected prime graph and composition factor isomorphic to L 2(81),” Proc. Int. Conf. on Group Theory Dedicated to the 70th Anniversary of V. V. Kabanov, Kabardino-Balkarian State Univ., Nalchik (2014), pp. 56–58.
A. S. Kondrat’ev, “Finite almost simple 5-primary groups and their Gruenberg–Kegel graphs,” Izv. Skorina Gomel State Univ., No. 3 (84), 58–60 (2014).
A. S. Kondrat’ev, “Finite almost simple 5-primary groups and their Gruenberg–Kegel graphs,” Sib. El. Mat. Izv., 11, 634–674 (2014); http://semr.math.nsc.ru/v11/p634-674.pdf.
A. Jafarzadeh and A. Iranmanesh, “On simple K n -groups for n = 5, 6,” in London Math. Soc. Lect. Note Ser., 340, C. M. Campbell et al. (Eds.), Cambridge Univ. Press, Cambridge (2007), pp. 517–526.
L. Zhang, W. Shi, H. Lu, D. Yu, and S. Chen, “OD-characterization of finite simple K 5-groups,” Preprint (2011).
The GAP Group, GAP—Groups, Algorithms, Programming, a System for Computational Discrete Algebra, Vers. 4.8.2 (2016); http://www.gap-system.org.
V. A. Kolpakova and A. S. Kondrat’ev, “Finite unsolvable 5-primary groups G with disconnected Gruenberg–Kegel graph such that |π(G/F(G))| ≤ 4,” Proc. Int. Conf. “Mal’tsev Readings,” Institute of Mathematics, Novosibirsk State University, Novosibirsk (2014), p. 64.
V. A. Kolpakova and A. S. Kondrat’ev, “Finite almost simple 6-primary groups and their Gruenberg–Kegel graphs,” Proc. Int. Conf. “Algebra and Applications” Dedicated to the 100th Anniversary of L. A. Kaluzhnin, Kabardino-Balkarian State Univ., Nalchik (2014), pp. 63–66.
G. Higman, “Finite groups in which every element has prime power order,” J. London Math. Soc., 32, 335–342 (1957).
Unsolved Problems in Group Theory, The Kourovka Notebook, 18th edn., Institute of Mathematics SO RAN, Novosibirsk (2014); http://www.math.nsc.ru/~alglog/18kt.pdf.
A. S. Kondrat’ev, “Recognizability of E 7(2) and E 7(3) by prime graph,” Trudy Inst. Mat. Mekh. UrO RAN, 20, No. 2, 223–229 (2014).
V. D. Mazurov, “Groups with prescribed orders of elements,” Izv. Ural. Gos. Univ., Mat. Mekh., 36, No. 7, 119–138 (2005).
A. S. Kondrat’ev, “Recognizability of 2 E 6(2) by prime graph,” Abelian Groups, Proc. Int. Symp. Dedicated to the 100th Anniversary of L. Ya. Kulikov, MGPU, Moscow (2014), pp. 35–37.
A. L. Gavrilyuk, I. V. Khramtsov, A. S. Kondrat’ev, and N. V. Maslova, “On realizability of a graph as the prime graph of a finite group,” Sib. El. Mat. Izv., 11, 246–257 (2014); http://semr.math.nsc.ru/v11/p246-257.pdf.
M. C. Lucido, “Groups in which the prime graph is a tree,” Boll. Unione Mat. Ital., Sez. B, Artic. Ric. Mat. (8), 5, No. 1, 131–148 (2002).
O. A. Alekseeva and A. S. Kondrat’ev, “Finite almost simple groups whose prime graphs have no triangles. I,” Trudy Inst. Mat. Mekh. UrO RAN, 21, No. 3, 3–12 (2015).
A. Gruber, T. M. Keller, M. L. Lewis, K. Naughton, and B. Strasser, “A characterization of the prime graphs of solvable groups,” J. Alg., 442, 397–422 (2015).
M. S. Lucido and A. R. Moghaddamfar, “Groups with complete prime graph connected components,” J. Group Theory, 7, No. 3, 373–384 (2004).
M. R. Zinov’eva and V. D. Mazurov, “Finite groups with disconnected prime graph,” Trudy Inst. Mat. Mekh. UrO RAN, 18, No. 3, 99–105 (2012).
M. R. Zinov’eva and A. S. Kondrat’ev, “Finite almost simple groups with prime graphs all of whose connected components are cliques,” Trudy Inst. Mat. Mekh. UrO RAN, 21, No. 3, 132–141 (2015).
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(A. S. Kondrat’ev) Supported by RFBR (project No. 13-01-00469), by the Complex Research Program of UrO RAN (project No. 15-16-1-5), and by the Program for State Aid of Leading RF Universities (Agreement No. 02.A03.21.0006 between the Ministry of Education and Science of the Russian Federation and the Ural Federal University, 27.08.2013).
Translated from Algebra i Logika, Vol. 55, No. 1, pp. 113–120, January-February, 2016.
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Kondrat’ev, A.S. Finite Groups with Given Properties of Their Prime Graphs. Algebra Logic 55, 77–82 (2016). https://doi.org/10.1007/s10469-016-9378-5
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DOI: https://doi.org/10.1007/s10469-016-9378-5