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Holt, Derek F.

Book review of: Gerhard O. Michler, Theory of finite simple groups. (English) Zbl 1292.00030

Bull. Am. Math. Soc., New Ser. 46, No. 1, 151-156 (2009).
Review of [Zbl 1146.20011].

MSC:

00A17 External book reviews
20-02 Research exposition (monographs, survey articles) pertaining to group theory
20D08 Simple groups: sporadic groups
20C34 Representations of sporadic groups
20C40 Computational methods (representations of groups) (MSC2010)

Citations:

Zbl 1146.20011

Software:

Magma; GAP; ATLAS Group Representations
Cite Review PDF
Full Text: DOI

References:

[1] J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson, Atlas of finite groups, Oxford University Press, Eynsham, 1985. Maximal subgroups and ordinary characters for simple groups; With computational assistance from J. G. Thackray. · Zbl 0568.20001
[2] -, ATLAS of finite group representations, http://web.mat.bham.ac.uk/atlas /index.html.
[3] Christoph Jansen, Klaus Lux, Richard Parker, and Robert Wilson, An atlas of Brauer characters, London Mathematical Society Monographs. New Series, vol. 11, The Clarendon Press, Oxford University Press, New York, 1995. Appendix 2 by T. Breuer and S. Norton; Oxford Science Publications. · Zbl 0831.20001
[4] Michael Aschbacher, The status of the classification of the finite simple groups, Notices Amer. Math. Soc. 51 (2004), no. 7, 736 – 740. · Zbl 1113.20302
[5] Michael Aschbacher and Stephen D. Smith, The classification of quasithin groups. I, Mathematical Surveys and Monographs, vol. 111, American Mathematical Society, Providence, RI, 2004. Structure of strongly quasithin \?-groups. Michael Aschbacher and Stephen D. Smith, The classification of quasithin groups. II, Mathematical Surveys and Monographs, vol. 112, American Mathematical Society, Providence, RI, 2004. Main theorems: the classification of simple QTKE-groups. · Zbl 1065.20023
[6] Michael Aschbacher and Stephen D. Smith, The classification of quasithin groups. I, Mathematical Surveys and Monographs, vol. 111, American Mathematical Society, Providence, RI, 2004. Structure of strongly quasithin \?-groups. Michael Aschbacher and Stephen D. Smith, The classification of quasithin groups. II, Mathematical Surveys and Monographs, vol. 112, American Mathematical Society, Providence, RI, 2004. Main theorems: the classification of simple QTKE-groups. · Zbl 1065.20023
[7] The GAP Group, GAP - Groups, Algorithms, and Programming, Version 4.4.10; 2007, (http://www.gap-system.org).
[8] Robert L. Griess Jr., The friendly giant, Invent. Math. 69 (1982), no. 1, 1 – 102. · Zbl 0498.20013 · doi:10.1007/BF01389186
[9] Daniel Gorenstein, Richard Lyons, and Ronald Solomon, The classification of the finite simple groups. Number 6. Part IV, Mathematical Surveys and Monographs, vol. 40, American Mathematical Society, Providence, RI, 2005. The special odd case. · Zbl 1069.20011
[10] Derek F. Holt, Bettina Eick, and Eamonn A. O’Brien, Handbook of computational group theory, Discrete Mathematics and its Applications (Boca Raton), Chapman & Hall/CRC, Boca Raton, FL, 2005. · Zbl 1091.20001
[11] Walter Feit and John G. Thompson, Solvability of groups of odd order, Pacific J. Math. 13 (1963), 775 – 1029. · Zbl 0124.26402
[12] Zvonimir Janko, A new finite simple group with abelian Sylow 2-subgroups and its characterization, J. Algebra 3 (1966), 147 – 186. · Zbl 0214.28003 · doi:10.1016/0021-8693(66)90010-X
[13] Peter Kleidman and Martin Liebeck, The subgroup structure of the finite classical groups, London Mathematical Society Lecture Note Series, vol. 129, Cambridge University Press, Cambridge, 1990. · Zbl 0697.20004
[14] J.J. Cannon and W. Bosma Handbook of Magma Functions, Edition 2.13, 2006, 4350 pages.
[15] Gerhard O. Michler, On the construction of the finite simple groups with a given centralizer of a 2-central involution, J. Algebra 234 (2000), no. 2, 668 – 693. Special issue in honor of Helmut Wielandt. · Zbl 0971.20009 · doi:10.1006/jabr.2000.8549
[16] R. A. Parker and R. A. Wilson, The computer construction of matrix representations of finite groups over finite fields, J. Symbolic Comput. 9 (1990), no. 5-6, 583 – 590. Computational group theory, Part 1. · Zbl 0742.20018 · doi:10.1016/S0747-7171(08)80075-2
[17] A. Seress, Permutation Group Algorithms, Chapman & Hall/CRC, 2005. · Zbl 1028.20002
[18] Charles C. Sims, The existence and uniqueness of Lyons’ group, Finite groups ’72 (Proc. Gainesville Conf., Univ. Florida, Gainesville, Fla., 1972) North-Holland, Amsterdam, 1973, pp. 138 – 141. North-Holland Math. Studies, Vol. 7.
[19] Ronald Solomon, A brief history of the classification of the finite simple groups, Bull. Amer. Math. Soc. (N.S.) 38 (2001), no. 3, 315 – 352. · Zbl 0983.20001
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