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Embeddings ofU 3(8),Sz(8) and the Rudvalis group in algebraic groups of typeE 7

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References

  • [AGo] Alperin, J., gorenstein, D.: The multiplicators of certain simple groups. Proc. Am. Math. Soc.17, 515–519 (1966)

    Google Scholar 

  • [Atlas] Conway, J.H., Curtis, R.T., Norton, S.P., Parker, R.A., Wilson, R.A.: An ATLAS of finite groups. Oxford: Clarendon 1985

    Google Scholar 

  • [B] Borovik, A.: The structure of finite subgroups of simple algebraic groups. Algebra Logic28, 249–279 (1989)

    Google Scholar 

  • [CLSS] Cohen, A.M., Liebeck, M.W., Saxl, J., Seitz, G.M.: The local maximal subgroups of the exceptional groups of Lie type. (Preprint 1988)

  • [CoGr1] Cohen, A.M., Griess, R.L., Jr.: On finite simple subgroups of the complex Lie group of typeE 8 In: Fong, P. (ed.) The Arcata Conf. on representations of finite groups. (Proc. Symp. Pure Math. Vol. 47, pp. 367–405) Providence, RI: Am. Math. Soc. 1987

    Google Scholar 

  • [CoGr2] Cohen, A.M., Griess, R.L., Jr.: Nonlocal Lie primitive subgroups of Lie groups. Can. J. Math., 14 pp. (to appear, 1991)

  • [CoWa1] Cohen, A.M., Wales, D.B.: Finite subgroups ofG 2(ℂ). Commun. Algebra11, 441–459 (1983)

    Google Scholar 

  • [CoWa2] Cohen, A.M., Wales, D.B.: Finite subgroups ofE 6(ℂ)2 andF 4(ℂ), 40 pp. (Preprint 1989)

  • [CuRe] Curtis, C., Reiner, I.: Representation theory of finite groups and associative algebras. New York: Interscience 1962

    Google Scholar 

  • [D] Dempwolff, U.: A characterization of the Rudvalis simple group of order 2143353·7·13·29 by the centralizer of noncentral involutions. J. Algebra32, 53–88 (1974)

    Google Scholar 

  • [FLM] Frenkel, I., Lepowsky, J., Meurman, A.: Vertex Operator Algebras and the Monster. (Pure Appl. Math.) New York London: Academic Press 1988

    Google Scholar 

  • [Go1] Gorenstein, D.: Finite Groups. New York: Harper and Row 1968

    Google Scholar 

  • [Go2] Gorenstein, D.: Finite Simple Groups: an Introduction to their Classification. London New York: Plenum 1982

    Google Scholar 

  • [Gr1] Griess, R.L., Jr.: Schur multipliers of groups of Lie type. Trans. Am. Math. Soc.183, 355–421 (1973)

    Google Scholar 

  • [Gr2] Griess, R.L., Jr.: Sporadic groups, code loops and nonvanishing cohomology, J. Pure Appl. Algebra44, 191–214 (1987)

    Google Scholar 

  • [Gr3] Griess, R.L., Jr.: Code loops and a large finite group containing triality forD 4, from. Rend. Circ. Mat. Palermo, II. Ser., Suppl.19, 79–98 (1988)

    Google Scholar 

  • [Gr4] Griess, R.L., Jr.: Elementary abelianp-subgroups of algebraic groups. Geom. Dedicata39, 253–305 (1991)

    Google Scholar 

  • [GMS] Griess, R.L., Jr., Mason, D., Seitz, G.M.: Bender groups as standard subgroups. Trans. Am. Math. Soc.238, 179–211 (1978)

    Google Scholar 

  • [Gruen] Gruenberg, K.W.: Cohomological Topics in Group Theory. Berlin Heidelberg New York: Springer 1970

    Google Scholar 

  • [Hig] Higman, G.: Suzuki 2-groups, Ill. J. Math.7, 79–96 (1963)

    Google Scholar 

  • [HL] Hiss, G., Lux, K.: Brauer Trees of Sporadic Groups. Oxford: Clarendon 1989

    Google Scholar 

  • [Hum] Humphries, J.: Introduction to Lie Algebras and Representation Theory, 3rd ed. Berlin Heidelberg New York: Springer 1980

    Google Scholar 

  • [Hup] Huppert, B.: Endliche Gruppen. Berlin Heidelberg New York: Springer 1967

    Google Scholar 

  • [Kac] Kac, V.G.: Infinite dimensional Lie algebras, 2-nd ed. Cambridge: Cambridge University Press 1985

    Google Scholar 

  • [KMR] Kleidman, P.B., Meierfrankenfeld, U., Ryba, A.J.E.: Construction of HiS and Ru inE 7(5). (Preprint 1989)

  • [KlRy] Kleidman, P.B., Ryba, A.J.E.: Kostant's Conjecture holds forE 7:L 2(37)<E 7(C). J. Algebra, 7 pp. (to appear)

  • [KlWi] Kleidman, P.B., Wilson, R.A.: Sporadic Subgroups of Finite Exceptional Groups of Lie Type. J. Algebra, 15 pp. (to appear)

  • [Land] Landrock, P.: Finite groups with a quasisimple component of type PSU (3, 2n) on elementary abelian form. Ill. J. Math.19, 198–230 (1975)

    Google Scholar 

  • [Lang] Lang, S.: Algebraic groups over finite fields. Am. Jour. Math.78, 555–563 (1956)

    Google Scholar 

  • [LiSa] Liebeck, M.W., Saxl, J.: On the orders of maximal subgroups of the finite exceptional groups of Lie type. Proc. Lond. Math. Soc.55, 299–330 (1987)

    Google Scholar 

  • [LiSe] Liebeck, M.W., Seitz, G.M.: Maximal subgroups of exceptional groups of Lie type, finite and algebraic. Geom. Dedicata35, 353–387 (1989)

    Google Scholar 

  • [Pa] Parker, R.A.: The computer calculation of modular characters (The ‘Meat axe’). In: Atkinson, M.D. (ed.) Computational Group Theory, pp. 267–274. New York London: Academic Press 1984

    Google Scholar 

  • [PaWi] Parker, R.A., Wilson, R.A.: The computer construction of matrix representations of finite groups over finite fields. J. Symb. Comput.9, 583–590 (1990)

    Google Scholar 

  • [Ru1] Rudvalis, A.: A new simple group of order 2143353·7·13·29. Notices Am. Math. soc.20, A-73 (1973)

    Google Scholar 

  • [Ru2] Rudvalis, A.: A rank 3 simple gorup of order 2143353·7·13·29. J. Algebra86, 181–218 (1984); II. Characters ofG andĜ. J. Algebra86, 219–258 (1984)

    Google Scholar 

  • [Ry] Ryba, A.J.E.: Matrix generators for the Held group. In: Tangora, M.C. (ed.) Computers in Algebra, pp. 135–141. New York: Dekker 1988

    Google Scholar 

  • [Se] Segal, G.: Unitary representations of some infinite dimensional groups. Commun. Math. Phys.80, 301–342 (1981)

    Google Scholar 

  • [SpSt] Springer, T.A., Steinberg, R.: Cojugacy Classes. In: Borel, A. et al. (eds) Seminar on Algebraic Groups and Related Finite Groups. (Lect. Notes Math., vol 131) Berlin Heidelberg New York: Springer 1970

    Google Scholar 

  • [St] Steinberg, R.: Automorphisms of Classical Lie Algebras. Pac. J. Math.11, 1119–1129 (1961)

    Google Scholar 

  • [Wi] Wilson, R.A.: The geometry and maximal subgroups of the simple groups of A. Rudvalis and J. Tis. Proc. Lond. Math. Soc.48, 533–563 (1984)

    Google Scholar 

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Dedicated to Armand Borel

Oblatum 5-XII-1991 & 24-II-1993

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Griess, R.L., Ryba, A.J.E. Embeddings ofU 3(8),Sz(8) and the Rudvalis group in algebraic groups of typeE 7 . Invent Math 116, 215–241 (1994). https://doi.org/10.1007/BF01231561

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