Abstract
We describe the spectra of simple and universal groups of Lie type E 7.
Similar content being viewed by others
References
Testerman D. M., “A 1-type overgroups of elements of order p in semisimple algebraic groups and the associated finite groups,” J. Algebra, 177, No. 1, 34–76 (1995).
Suzuki M., “On a class of doubly transitive groups,” Ann. Math. (2), 75, 105–145 (1962).
Brandl R. and Shi W. J., “A characterization of finite simple groups with abelian Sylow 2-subgroups,” Ric. Mat., 42, No. 1, 193–198 (1993).
Deng H. W. and Shi W. J., “The characterization of Ree groups 2 F 4(q) by their element orders,” J. Algebra, 217, No. 1, 180–187 (1999).
Kantor W. M. and Seress A., “Prime power graphs for groups of Lie type,” J. Algebra, 247, No. 2, 370–434 (2002).
Deriziotis D. I., Conjugacy Classes of Centralizers of Semisimple Elements in Finite Groups of Lie Type, Univ. Essen Fachbereich Math., Essen (1984) (Vorlesungen Fachbereich Math. Univ. Essen; V. 11).
Vasil’ev A. V. and Staroletov A. M., “Recognizability of groups G2(q) by spectrum,” Algebra and Logic, 52, No. 1, 1–14 (2013).
Grechkoseeva M.A. and Zvezdina M. A., “On spectra of automorphic extensions of finite simple groups F4(q) and 3D4(q),” J. Algebra Appl., 15, No. 4, 1650168 (2016).
Buturlakin A. A., “Spectra of finite simple groups E6(q) and 2E6(q),” Algebra and Logic, 52, No. 3, 188–202 (2013).
Buturlakin A. A., “Spectra of finite linear and unitary groups,” Algebra and Logic, 47, No. 2, 91–99 (2008).
Buturlakin A. A., “Spectra of finite symplectic and orthogonal groups,” Sib. Adv. Math., 21, No. 3, 176–210 (2011).
Deriziotis D. I. and Fakiolas A. P., “The maximal tori in the finite Chevalley groups of type E6, E7 and E8,” Comm. Algebra, 19, No. 3, 889–903 (1991).
Carter R. W., Finite Groups of Lie Type. Conjugacy Classes and Complex Characters, John Wiley and Sons, Chichester, New York, etc. (1985).
Carter R. W., “Centralizers of semisimple elements in finite groups of Lie type,” Proc. Lond. Math. Soc. (3), 37, 491–507 (1978).
Deriziotis D. I., “The centralizers of semisimple elements of the Chevalley groups E7 and E8,” Tokyo J. Math., 6, No. 1, 191–216 (1983).
Oshima T., “A classification of subsystems of a root system,” arXiv:math/0611904.
Zavartnitsine A. V., “Structure of the maximal tori in spin groups,” Sib. Math. J., 56, No. 3, 425–434 (2015).
Bosma W., Cannon J., and Playoust C., “The Magma algebra system. I. The user language,” J. Symb. Comput., 24, No. 3–4, 235–265 (1997).
Gorenstein D., Lyons R., and Solomon R., The Classification of the Finite Simple Groups. Number 3, Amer. Math. Soc., Providence (1998) (Math. Surveys and Monogr.; V. 40).
Deriziotis D. I. and Michler G. O., “Character table and blocks of finite simple triality groups 3D4(q),” Trans. Amer. Math. Soc., 303, 39–70 (1987).
Buturlakin A. A. and Grechkoseeva M. A., “The cyclic structure of maximal tori of the finite classical groups,” Algebra and Logic, 46, No. 2, 73–89 (2007).
Author information
Authors and Affiliations
Corresponding author
Additional information
Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 57, No. 5, pp. 988–998, September–October, 2016; DOI: 10.17377/smzh.2016.57.505.
Rights and permissions
About this article
Cite this article
Buturlakin, A.A. Spectra of the finite simple groups E 7(q). Sib Math J 57, 769–777 (2016). https://doi.org/10.1134/S0037446616050050
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0037446616050050