×

zbMATH — the first resource for mathematics

The friendly giant. (English) Zbl 0498.20013

MSC:
20D05 Finite simple groups and their classification
20D08 Simple groups: sporadic groups
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] Alperin, J., Gorenstein, D.: A vanishing theorem for cohomology. Proc. Amer. Math. Soc.32, 87-88 (1972) · Zbl 0249.18026
[2] Artin, E.: Geometric Algebra. New York:Interscience 1957 · Zbl 0077.02101
[3] Aschbacher, M.: private communication
[4] Aschbacher, M., Seitz, G.: On groups with a standard component of known type. Osaka J. Math.13, 439-482 (1976) · Zbl 0374.20015
[5] Borel, A.: Seminar on algebraic groups and related finite groups. Lecture Notes in Mathematics, vol. 131. Berlin-Heidelberg-New York: Springer 1973 · Zbl 0272.00007
[6] Brauer, R., Nesbitt, C.: On the modular representation of groups of finite order, I, University of Toronto Studies, No. 4, 21 pp. (1937) · Zbl 0018.29504
[7] Burgoyne, N., Fong, P.: Schur multipliers of the Mathieu groups. Nagoya Math. J.27, 733-745 (1966); Correction, ibid31, 297-304 (1968) · Zbl 0171.28801
[8] Burgoyne, N., Griess, R., Lyons, R.: Maximal subgroups and automorphisms of Chevalley groups. Pacific J. of Math.71, 365-403 (1977) · Zbl 0334.20022
[9] Carter, R.: Simple groups of Lie type. New York: Wiley ? Interscience 1972 · Zbl 0248.20015
[10] Conway, J.: A group of order 8, 315, 553, 613, 086, 720, 000. Bull. L.M.S.1, 79-88 (1969) · Zbl 0186.32304
[11] Conway, J.: Three lectures on exceptional groups in Higman-Powell, pp. 215-247. Finite simple groups. London: Academic Press 1971
[12] Conway, J., Guy, M., Patterson, N.: The characters and conjugacy classes of {\(\cdot\)}0, {\(\cdot\)}1, {\(\cdot\)}2, {\(\cdot\)}3 and Suz. unpublished
[13] Conway, J., Norton, S.: Monstrous moonshine. Bull. London Math. Soc.11, 303-339 (1979) · Zbl 0424.20010
[14] Curran, P.: Fixed point free action on a class of abelian groups. Proc. Amer. Math. Soc.57, 189-193 (1976) · Zbl 0335.18011
[15] Curtis, C., Reiner, I.: Representation theory of finite groups and associative algebra. New York: Interscience 1962 · Zbl 0131.25601
[16] Dempwolf, U.: On extensions of an elementary abelian group of order 25 byGL(5, 2), Rendiconti del Seminario Matematico della Universita di Padova48, 359-364 (1973)
[17] Dickson, L.E.: Linear groups. New York: Dover 1968
[18] Dieudonne, J.: La geometrie des groups classiques. Berlin-Heidelberg-New York: Springer 1971
[19] Finkelstein, L., Solomon, R.: Standard components of typeM 12 and.3. Osaka J. Math.16, 759-774 (1979) · Zbl 0429.20018
[20] Fischer, B.: Private correspondence. 1971
[21] Fischer, B.: Privately circulated note. 1973
[22] Fischer, B., Livingstone, D., Thorne, M.P.: The character table ofF 1. unpublished
[23] Fong, P.: On decomposition numbers ofJ 1 andR(q), Instituto Nazionale di Alta Mathematica, Symposia Mathematica, volume XII, 415-422 (1973)
[24] Gilman, R., Griess, R.: A characterization of finite groups of Lie type in characteristic 2. submitted to J. of Algebra · Zbl 0508.20010
[25] Glauberman, G.: Central elements in corefree groups. J. of Algebra4, 403-420 (1966) · Zbl 0145.02802
[26] Goldschmidt, D.: 2-fusion in finite groups. Annals of Math.99, 70-117 (1974) · Zbl 0276.20011
[27] Gorenstein, D.: Finite Groups. New York: Harper and Row 1968 · Zbl 0185.05701
[28] Gorenstein, D., Walter, J.: The characterization of finite groups with dihedral Sylow 2-subgroups, I, II and III. J. of Algebra2, 85-151; 218-270; 354-293 (1965) · Zbl 0192.11902
[29] Griess, R.: A construction ofF 1 as automorphisms of a 196,883 dimensional algebra. Proc. Natl. Acad. Sci. USA78, 689-691 (1981) · Zbl 0452.20020
[30] Griess, R.: A subgroup of order 215|GL(5,2)| inE 8(?), the Dempwolff group and Aut (D 8 ?D 8 ?D 8). J. of Algebra40, 271-279 (1976) · Zbl 0348.20011
[31] Griess, R.: Automorphisms of extra special groups and nonvanishing degrees 2 cohomology. Pacific J. of Math.28, 403-422 (1973) · Zbl 0283.20028
[32] Griess, R.: Schur multipliers of finite simple groups of Lie type. Trans. Amer. Math. Soc.183, 355-421 (1973) · Zbl 0297.20023
[33] Griess, R.: Schur multipliers of some sporadic simple groups. J. of Algebra32, 445-466 (1974) · Zbl 0303.20010
[34] Griess, R.: Schur multipliers of the known finite simple groups I. Bull. Amer. Math. Soc.78, 78-71 (1972) · Zbl 0263.20008
[35] Griess, R.: Schur multipliers of the known finite simple groups II, in the Santa Cruz Conference on Finite Groups, edited by B. Cooperstein and G. Mason · Zbl 0448.20014
[36] Griess, R.: Structure of the Friendly Giant. In preparation · Zbl 0498.20013
[37] Griess, R.: Structure of the monster simple group. Proceedings of the Conference in Finite Groups. New York: Academic Press 1976 · Zbl 0356.20021
[38] Griess, R., Solomon, R.: Finite groups with unbalancing 2-components of {L 3(4),He}-type. J. Algebra60, 92-125 (1979) · Zbl 0428.20007
[39] Gruenberg, K.: Cohomological topics in group theory. Berlin-Heidelberg-New York: Springer 1970 · Zbl 0205.32701
[40] Harada, K.: On the simple groupF of order 2143656. 7. 11. 19. Proc. of a Conference on Finite Groups, pp. 119-276
[41] Held, D.: The simple groups related toM 24. J. Algebra13, 253-296 (1969) · Zbl 0182.04302
[42] Jacobson, N.: The theory of rings. Amer. Math. Soc., Providence 1943 · Zbl 0060.07302
[43] Janko, Z.: A new finite simple group with abelian Sylow 2-subgroups and its characterization. J. of Algebra3, 147-186 (1966) · Zbl 0214.28003
[44] Janko, Z.: Inst. Natl. Alta Math. Symposia Math. Odensi Gubbio,1, 25-64 (1968)
[45] Jordan, C.: Traité des substitutions et des èquations algébriques. Paris: Gautheirs-Villars 1870
[46] Kusefoglu, A.: Cohomology of finite orthogonal groups. I: J. of Algebra56, 207-220; II: J. of Algebra67, 88-109 (1980) · Zbl 0404.20042
[47] Kusefoglu, A.: Thesis, University of Michigan 1976
[48] Lang, S.: Algebraic groups over finite fields. Amer. J. of Math.78, 555-563 (1956) · Zbl 0073.37901
[49] Leech, J.: Notes on sphere packings. Can. J. Math.19, 251-267 (1967) · Zbl 0162.25901
[50] Leech, J.: Some sphere packings in higher space. Can. J. Math.16, 657-682 (1964) · Zbl 0142.20201
[51] Leon, J.S., Sims, C.C.: The existence and uniqueness of a simple group generated by {3, 4}-transpositions. Bull. Amer. Math. Soc.83, 1039-1040 (1977) · Zbl 0401.20009
[52] McKay, J., Wales, D.: The multipliers of the simple groups of order 604,800, and 50,232,960. J. of Algebra17, 262-272 (1971) · Zbl 0215.10202
[53] Norton, S.: Thesis, University of Cambridge 1975
[54] Norton, S.: Transposition algebras and the groupF 24, to appear
[55] Niemeyer, H.V.: Definite Quadratische Formen der Diskriminante 1 und Dimension 24. Doctoral Dissertation. Göttingen, 1968
[56] Patterson, N.J.: On Conway’s group .0 and some subgroups. Thesis, University of Cambridge, 1972
[57] Pollatsek, H.K.: Cohomology groups of some linear groups over fields of characteristics 2, Ill. J. of Math.15, 393-417 (1971) · Zbl 0218.20039
[58] Robinson, D.: The vanishing of certain homology and cohomology groups. J. of Pure and Applied Algebra7, 145-167 (1976) · Zbl 0329.20032
[59] Ronan, M.A., Smith, S.D.: 2-local geometries for some sporadic groups. The Santa Cruz Conference on Finite Groups, edited by B. Cooperstein and G. Mason. Amer. Math. Soc. Providence, 1980 · Zbl 0478.20015
[60] Seitz, G.: Standard subgroups in finite groups. Finite simple groups II, M.J. Collins, (ed.). London: Academic Press 1980 · Zbl 0458.20011
[61] Smith, S.: Nonassociative commutative algebras for triple covers of 3-transposition groups. Michigan Math. J.24, 273-287 (1977) · Zbl 0391.20011
[62] Smith, S.: The classification of finite groups with large extraspecial 2-subgroups. The Santa Cruz Conference on Finite Groups, edited by B. Cooperstein and G. Mason. Amer. Math. Soc., Providence, 1980 · Zbl 0451.20014
[63] Smith, S.: Large extraspecial subgroups of width 4 and 6. J. of Algebra58, 251-281 (1979) · Zbl 0411.20009
[64] Steinberg, R.: Generators, relations, and coverings of algebraic groups II. to appear · Zbl 0468.20038
[65] Steinberg, R.: Lectures on Chevalley groups, lecture notes, Mathematics Department, Yale University · Zbl 1196.22001
[66] Steinberg, R.: Representation of algebraic groups. Nagoya Math. J.22, 33-56 (1963) · Zbl 0271.20019
[67] Stroth, G.: Eine Kennzeichnung der Gruppen2 E 6(2 n ). J. of Algebra35, 534-547 (1975) · Zbl 0316.20009
[68] Suzuki, M.: On a class of doubly transitive groups. Ann. of Math.75, 105-145 (1962) · Zbl 0106.24702
[69] Thompson, J.: A simple subgroup ofE 8(3). Finite Groups, Iwahori, N. (ed.). Japan Society for Promotion of Science, Tokyo, 1976
[70] Thompson, J.: Nonsolvable finite groups all of whose local subgroups are solvable. Bull. Amer. Math. Soc.74, 383-437 (1968) · Zbl 0159.30804
[71] Thompson, J.: Uniqueness of the Fischer-Griess monster. Bull. London Math. Soc.11, 340-346 (1979) · Zbl 0424.20012
[72] Timmesfeld, F.: Groups generated by root involutions. I, II. J. of Algebra33, 75-135 (1975);35, 367-441 (1975) · Zbl 0293.20026
[73] Timmesfeld, F.: Groups ofGF(2)-type and related problems. Finite Simple Groups II, Collins, M.J. (ed.). London: Academic Press 1980 · Zbl 0458.20016
[74] Tood, J.: A representation of the Mathieu groupM 24 as a collineation group. Annali di Mathematica Pura ed Applicata.71, 199-238 (1966) · Zbl 0144.26204
[75] Walter, J.: The characterization of finite groups with abelian Sylow 2-groups. Ann. of Math.89, 405-514 (1969) · Zbl 0184.04605
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.