Hostname: page-component-848d4c4894-wzw2p Total loading time: 0 Render date: 2024-05-08T19:52:42.649Z Has data issue: false hasContentIssue false
  • English
  • Français

Non-Local Lie Primitive Subgroups of Lie Groups

Published online by Cambridge University Press:  20 November 2018

Arjeh M. Cohen  and
Robert L. Griess Jr.
Arjeh M. Cohen
Affiliation:
Centre for Mathematics and Computer Science, Kruislaan 413, 1098 SJ Amsterdam
Robert L. Griess Jr.
Affiliation:
Department of Mathematics, University of Michigan, Angell Hall, Ann Arbor, MI 48104
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Borovik found a Lie primitive subgroup of E8(ℂ) isomorphic to (Alt5 × Sym6) : 2. In this note, we provide a short proof of existence and his result that the conjugacy class of this subgroup is the only one among those of non-local Lie primitive subgroups of finite dimensional simple complex Lie groups having a socle with more than one simple factor.

Keywords

22E2022E46
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 1 , 01 February 1993 , pp. 88 - 103
Copyright
Copyright © Canadian Mathematical Society 1993

References

[Adams 1986] Adams, J.F., 2-tori in exceptional Lie groups, preprint.Google Scholar
[Aleks 1974] Alekseevskii, A.V., Finite commutative Jordan subgroups of complex simple Lie groups, Funct. Anal, and its Appl. 8(1974), 277–279.Google Scholar
[Aschb 1984] Aschbacher, M., On the maximal subgroups of the finite classical groups, Inventiones Math. 76(1984), 469–514.Google Scholar
[Atlas 1985] Conway, J.H., Curtis, R.T., Norton, S.P., Parker, R.P. and Wilson, R.A., Atlas of finite groups, Clarendon Press, Oxford, 1985.Google Scholar
[Blich 1917] Blichfeldt, H.F., Finite Collineation Groups, University of Chicago Press, 1917.Google Scholar
[Borov 1989] Borovik, A., The structure of finite subgroups of simple algebraic groups, Algebra and Logic 28(1989), 249–279.Google Scholar
[Bourb 1968] Bourbaki, N., Groupes et algèbres de Lie, Chap. 4,5 et 6, Hermann, Paris, 1968.Google Scholar
[Brauer 1968] Brauer, R.D., On simple subgroups of order 5.3a.2/?, Bull. Amer. Math. Soc. 74(1968) 900-903.Google Scholar
[CLSS 1992] Cohen, A.M., Liebeck, M.W., Saxl, J. and Seitz, G.M., The local maximal subgroups of the exceptional groups of Lie type, Proceedings London Math. Soc. (1992), to appear.Google Scholar
[CoGr 1987] Cohen, A.M. and Griess, R.L., Jr., On finite simple subgroups of the complex Lie group of type Es, Proc. of Symposia in Pure Math. 47(1987), 367–405.Google Scholar
[CoGrLi 1992] Cohen, A.M., Griess, R.L., Jr. and Bert Lisser, The group L(2,61) embeds in the Lie group of type E%, Comm. in Algebra (1992), to appear.Google Scholar
[CoSe 1987] Cohen, A.M. and Seitz, G.M., The r-rank of the groups of exceptional Lie type, Indagationes Math 90(1987), 251–259.Google Scholar
[CoWa 1983] Cohen, A.M. and Wales, D.B., Finite subgroups of G2(C), Comm. Algebra 11(1983), 441–459.Google Scholar
[CoWa 1989] Finite subgroups of £6(C) and F4(C), preprint.Google Scholar
[Dynk 1957] Dynkin, E.B., Semisimple subalgebras of semisimple Lie algebras, Amer. Math. Soc. Transi. 6(1957), 111–244.Google Scholar
[Glau 1966] Glauberman, G., Central elements in corefree groups, Jour, of Algebra 4(1966), 403–420.Google Scholar
[Gor 1968] Gorenstein, D., Finite groups, Harper and Row, New York, 1968.Google Scholar
[Gr 1991] Griess, R.L., Jr., Elementary abelian p-subgroups of algebraic Groups, Geometria Dedicata 39(1991), 253–305.Google Scholar
[GrRy 1992] Griess, R.L., Jr. and E, A.J.. Ryba, Embeddings of £/3(8), Sz(8) and the Rudvalls group in algebraic groups of type E1, (1992), submitted.Google Scholar
[Kac 1985] Kac, V., Infinite Dimensional Lie algebras, Cambridge University Press, Cambridge, 1985.Google Scholar
[KMR 1989] Kleidman, P., Meierfrankenfeld, U. & Ryba, A. Constructiono/HiS andRu in E1(5),preprint.Google Scholar
[LiSe 1989] Liebeck, M.W. and Seitz, G.M., Maximal subgroups of exceptional groups of Lie type, finite and algebraic, Geom. Dedicata 35(1989), 353–387.Google Scholar
[Tits 1959] Tits, J., Sur la trialité et certains groupes qui s'en déduisent, Publ. Math. I.H.E.S. 2(1959), 14–60.Google Scholar