Geodesic
Finite almost simple $5$-primary groups and their Gruenberg--Kegel graphs
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 634-674.

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

The finite almost simple $5$-primary groups and their Gruenberg–Kegel graphs are determined. In addition, a list of finite simple $5$-primary groups is essentially refined.
Keywords: finite almost simple group, prime graph, $5$-primary group. 
@article{SEMR_2014_11_a19,
     author = {Anatoly S. Kondrat'ev},
     title = {Finite almost simple $5$-primary groups and their {Gruenberg--Kegel} graphs},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {634--674},
     publisher = {mathdoc},
     volume = {11},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2014_11_a19/}
}
TY  - JOUR
AU  - Anatoly S. Kondrat'ev
TI  - Finite almost simple $5$-primary groups and their Gruenberg--Kegel graphs
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2014
SP  - 634
EP  - 674
VL  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2014_11_a19/
LA  - en
ID  - SEMR_2014_11_a19
ER  - 
%0 Journal Article
%A Anatoly S. Kondrat'ev
%T Finite almost simple $5$-primary groups and their Gruenberg--Kegel graphs
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2014
%P 634-674
%V 11
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2014_11_a19/
%G en
%F SEMR_2014_11_a19
Anatoly S. Kondrat'ev. Finite almost simple $5$-primary groups and their Gruenberg--Kegel graphs. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 634-674. http://geodesic.mathdoc.fr/item/SEMR_2014_11_a19/

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

[2] R. W. Carter, Simple groups of Lie type, Wiley, London, 1972 | MR | Zbl

[3] R. W. Carter, “Conjugacy classes in the Weyl group”, Compositio Mathematica, 25:1 (1972), 1–59 | MR | Zbl

[4] R. W. Carter, “Centralizers of semisimple elements in the finite classical groups”, Proc. London Math. Soc. (3), 42:1 (1981), 1–41 | DOI | MR | Zbl

[5] R. W. Carter, Finite groups of Lie type, conjugacy classes and complex characters, Wiley, London, 1985 | MR | Zbl

[6] Z. M. Chen, W. J. Shi, “On simple $C_{pp}$-groups”, J. Southwest China Normal Univ., 18:3 (1993), 249–256 (in Chinese)

[7] 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

[8] S. Dolfi, E. Jabara, M. S. Lucido, “$C55$-groups”, Siberian Math. J., 45:6 (2004), 1053–1062 | DOI | MR | Zbl

[9] G. C. Gerono, “Note sur la resolution en nombres entiers et positifs de l'equation $x^m = y^n-1$”, Nouv. Ann. Math. (2), 9 (1870), 469–471

[10] D. Gorenstein, R. Lyons, R. Solomon, The classification of the finite simple groups, v. 3, Math. Surv. Monogr., 40.3, Amer. Math. Soc., Providence, RI, 1998 | MR | Zbl

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

[12] A. Jafarzadeh, A. Iranmanesh, “On simple $K_n$-groups for $n=5,6$”, London Math. Soc. Lecture Note Ser., 340, 2007, 517–526 | MR | Zbl

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

[14] A. S. Kondrat'ev, “Prime graph components of finite simple groups”, Math. USSR Sb., 67:1 (1990), 235–247 | DOI | MR | Zbl

[15] A. S. Kondrat'ev, “On finite groups with small prime spectrum”, Groups and graphs, Matem. Forum (Itogi nauki. Yug Rossii), 6, YuMI VNZ RAN and RSO-A, Vladikavkaz, 2012, 52–70 (In Russian)

[16] A. S. Kondrat'ev, I. V. Khramtsov, “On finite triprimary groups”, Trudy IMM UrO RAN, 16, no. 3, 2010, 150–158 (In Russian)

[17] A. S. Kondrat'ev, I. V. Khramtsov, “On finite tetraprimary groups”, Proc. Steklov Inst. Math., 279, 2012, S43–S61

[18] A. S. Kondrat'ev, I. V. Khramtsov, “On finite nonsimple triprimary groups with disconnected prime graph”, Sib. Elektron. Mat. Izv., 9 (2012), 472–477 (In Russian) | MR

[19] A. S. Kondrat'ev, I. V. Khramtsov, “The complete reducibility of some GF(2)A7-modules”, Trudy IMM UrO RAN, 18, no. 3, 2012, 139–143 (In Russian)

[20] V. M. Levchuk, Ya. N. Nuzhin, “The structure of Ree groups”, Algebra i Logika, 24:1 (1985), 26–41 (in Russian) | DOI | MR | Zbl

[21] M. Li, All the $C_{pp}$ simple groups on certain conditions, Southwest University, Chongqing, 2008

[22] W. Ljunggren, “Ueber die Gleichungen $1+Dx^2=2y^n$ und $1+Dx^2=4y^n$”, Norsk Vid. Selsk. Forh., 15:30 (1942), 115–118 | MR | Zbl

[23] M. S. Lucido, “Prime graph components of finite almost simple groups”, Rend. Sem. Mat. Univ. Padova, 102 (1999), 1O–22 ; addendum, Rend. Sem. Mat. Univ. Padova, 107 (2002), 189–190 | MR | Zbl | MR | Zbl

[24] W. J. Shi, “The quantitative peoperty of finite groups”, J. Xuzhou Normal University (Natural Science Edition), 27:2 (2009), 1–15 | MR

[25] A. V. Vasil'ev, E. P. Vdovin, “An adjacency criterion for the prime graph of a finite simple group”, Algebra and Logic, 44:6 (2005), 381–406 | DOI | MR | Zbl

[26] A. V. Vasil'ev, E. P. Vdovin, “Cocliques of maximal size in the prime graph of a finite simple group”, Algebra and Logic, 50:4 (2011), 291–322 | DOI | MR | Zbl

[27] J. S. Williams, “Prime graph components of finite groups”, J. Algebra, 69:2 (1981), 487–513 | DOI | MR | Zbl

[28] L. Zhang, W. Shi, H. Lv, D. Yu, S. Chen, $OD$-characterization of finite simple $K_5$-groups, Preprint, 2011

[29] K. Zsigmondy, “Zur Theorie Potenzreste”, Monatsh. Math. Phys., 3:1 (1892), 265–284 | DOI | MR | Zbl