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Book Information:

Author: Michael Aschbacher
Title: 3-Transposition groups
Additional book information: Cambridge University Press, 1997, 260+vii pp., ISBN 0-521-57196-0, $49.94$

Michael Aschbacher, On finite groups generated by odd transpositions. I, Math. Z. 127 (1972), 45–56. MR 310058, DOI 10.1007/BF01110103

Michael Aschbacher, On finite groups of component type, Illinois J. Math. 19 (1975), 87–115. MR 376843

Michael Aschbacher, On finite groups in which the generalized Fitting group of the centralizer of some involution is extraspecial, Illinois J. Math. 21 (1977), no. 2, 347–364. MR 442089

Michael Aschbacher, Finite group theory, Cambridge Studies in Advanced Mathematics, vol. 10, Cambridge University Press, Cambridge, 1986. MR 895134

Michael Aschbacher, Sporadic groups, Cambridge Tracts in Mathematics, vol. 104, Cambridge University Press, Cambridge, 1994. MR 1269103, DOI 10.1017/CBO9780511665585

Richard Brauer, On the structure of groups of finite order, Proceedings of the International Congress of Mathematicians, Amsterdam, 1954, Vol. 1, Erven P. Noordhoff N. V., Groningen; North-Holland Publishing Co., Amsterdam, 1957, pp. 209–217. MR 0095203

J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson, $\Bbb {ATLAS}$ of finite groups, Oxford University Press, Eynsham, 1985. Maximal subgroups and ordinary characters for simple groups; With computational assistance from J. G. Thackray. MR 827219

H. Cuypers and J. I. Hall, The $3$-transposition groups with trivial center, J. Algebra 178 (1995), no. 1, 149–193. MR 1358261, DOI 10.1006/jabr.1995.1344

Bernd Fischer, Distributive Quasigruppen endlicher Ordnung, Math. Z. 83 (1964), 267–303 (German). MR 160845, DOI 10.1007/BF01111162

Bernd Fischer, A characterization of the symmetric groups on 4 and 5 letters, J. Algebra 3 (1966), 88–98. MR 194498, DOI 10.1016/0021-8693(66)90020-2

Bernd Fischer, Finite groups generated by $3$-transpositions. I, Invent. Math. 13 (1971), 232–246. MR 294487, DOI 10.1007/BF01404633

Daniel Gorenstein, Finite simple groups, University Series in Mathematics, Plenum Publishing Corp., New York, 1982. An introduction to their classification. MR 698782

George Glauberman, On loops of odd order, J. Algebra 1 (1964), 374–396. MR 175991, DOI 10.1016/0021-8693(64)90017-1

George Glauberman, Central elements in core-free groups, J. Algebra 4 (1966), 403–420. MR 202822, DOI 10.1016/0021-8693(66)90030-5

Michio Suzuki, On characterizations of linear groups. I, II, Trans. Amer. Math. Soc. 92 (1959), 191–219. MR 108536, DOI 10.1090/S0002-9947-1959-0108536-9

Franz Timmesfeld, Finite simple groups in which the generalized Fitting group of the centralizer of some involution is extraspecial, Ann. of Math. (2) 107 (1978), no. 2, 297–369. MR 486255, DOI 10.2307/1971146

F. G. Timmesfeld, Groups generated by $k$-root subgroups, Invent. Math. 106 (1991), no. 3, 575–666. MR 1134484, DOI 10.1007/BF01243925

18.

M.-M. Virotte-Ducharme, Couple fischériens presque simple, Thèse, Université Paris 7, 1985.

G. E. Wall, On the conjugacy classes in the unitary, symplectic and orthogonal groups, J. Austral. Math. Soc. 3 (1963), 1–62. MR 0150210

Richard Weiss, A uniqueness lemma for groups generated by $3$-transpositions, Math. Proc. Cambridge Philos. Soc. 97 (1985), no. 3, 421–431. MR 778676, DOI 10.1017/S030500410006299X

21.

F. Zara, Classification des couples fischeriens, Thèse Université de Picardie, 1984.

Review Information:

Reviewer: Jonathan I. Hall
Affiliation: Michigan State University
Email: jhall@math.msu.edu

Journal: Bull. Amer. Math. Soc. 35 (1998), 161-169
DOI: https://doi.org/10.1090/S0273-0979-98-00741-1
Keywords: Sporadic groups, finite simple groups, $3$-transposition groups
Review copyright: © Copyright 1998 American Mathematical Society