Spectra of groups~$E_8(q)$

A. A. Buturlakin

Algebra i logika, Tome 57 (2018) no. 1, pp. 3-13.

Résumé

We give a description of spectra of finite simple and universal groups of Lie type $E_8$.

Détail

Keywords: spectrum of group, order of element, exceptional groups of Lie type.

Bibliographie

[1] D. M. Testerman, “$A_1$-type overgroups of elements of order $p$ in semisimple algebraic groups and the associated finite groups”, J. Algebra, 177:1 (1995), 34–76 | DOI | MR | Zbl

[2] M. Suzuki, “On class of double transitive groups”, Ann. Math. (2), 75:1 (1962), 105–145 | DOI | MR | Zbl

[3] R. Brandl, W. Shi, “A characterization of finite simple groups with abelian Sylow 2-subgroups”, Ric. Mat., 42:1 (1993), 193–198 | MR | Zbl

[4] H. Deng, W. Shi, “The characterization of Ree groups $^2F_4(q)$ by their element orders”, J. Algebra, 217:1 (1999), 180–187 | DOI | MR | Zbl

[5] W. M. Kantor, A. Seress, “Prime power graphs for groups of Lie type”, J. Algebra, 247:2 (2002), 370–434 | DOI | MR | Zbl

[6] D. I. Deriziotis, Conjugacy classes of centralizers of semisimple elements in finite groups of Lie type, Vorlesungen Fachbereich Math. Univ. Essen, 11, Essen, 1984 | MR | Zbl

[7] A. V. Vasilev, A. M. Staroletov, “Raspoznavaemost grupp $G_2(q)$ po spektru”, Algebra i logika, 52:1 (2013), 3–21 | MR | Zbl

[8] M. A. Grechkoseeva, M. A. Zvezdina, “On spectra of automorphic extensions of finite simple groups $F_4(q)$ and $^3D_4(q)$”, J. Algebra Appl., 15:9 (2016), Article ID 1650168 | DOI | MR | Zbl

[9] A. A. Buturlakin, “Spektry konechnykh prostykh grupp $E_6(q)$ i $^2E_6(q)$”, Algebra i logika, 52:3 (2013), 284–304 | MR | Zbl

[10] A. A. Buturlakin, “Spektry konechnykh prostykh grupp $E_7(q)$”, Sib. matem. zh., 57:5 (2016), 988–998 | DOI | MR | Zbl

[11] A. A. Buturlakin, “Spektry konechnykh lineinykh i unitarnykh grupp”, Algebra i logika, 47:2 (2008), 157–173 | MR | Zbl

[12] A. A. Buturlakin, “Spektry konechnykh simplekticheskikh i ortogonalnykh grupp”, Matem. tr., 13:2 (2010), 33–83 | MR | Zbl

[13] D. I. Deriziotis, A. P. Fakiolas, “The maximal tori in the finite Chevalley groups of type $E_6$, $E_7$ and $E_8$”, Commun. Algebra, 19:3 (1991), 889–903 | DOI | MR | Zbl

[14] R. W. Carter, Finite groups of Lie type. Conjugacy classes and complex characters, Pure Appl. Math., A Wiley-Interscience Publ., John Wiley and Sons, Chichester–New York etc., 1985 | MR | Zbl

[15] R. W. Carter, “Centralizers of semisimple elements in finite groups of Lie type”, Proc. Lond. Math. Soc. III Ser., 37:3 (1978), 491–507 | DOI | MR | Zbl

[16] D. I. Deriziotis, “The centralizers of semisimple elements of the Chevalley groups $E_7$ and $E_8$”, Tokyo J. Math., 6:1 (1983), 191–216 | DOI | MR | Zbl

[17] T. Oshima, A classification of subsystems of a root system, arXiv: math/0611904[math.RT]

[18] D. Gorenstein, R. Lyons, R. Solomon, The classification of the finite simple groups. Part I. Chapter A: Almost simple $K$-groups, Math. Surv. Monogr., 40, no. 3, Am. Math. Soc., Providence, RI, 1998 | MR | Zbl

[19] W. Bosma, J. Cannon, C. Playoust, “The Magma algebra system. I. The user language”, J. Symb. Comput., 24:3/4 (1997), 235–265 | DOI | MR | Zbl

[20] A. V. Zavarnitsin, “Stroenie maksimalnykh torov v spinornykh gruppakh”, Sib. matem. zh., 56:3 (2015), 537–548 | DOI | MR | Zbl

[21] D. I. Deriziotis, G. O. Michler, “Character table and blocks of finite simple triality groups $^3D_4(q)$”, Trans. Am. Math. Soc., 303:1 (1987), 39–70 | MR | Zbl

[22] A. A. Buturlakin, M. A. Grechkoseeva, “Tsiklicheskoe stroenie maksimalnykh torov v konechnykh klassicheskikh gruppakh”, Algebra i logika, 46:2 (2007), 129–156 | MR | Zbl