%%% ==================================================================== %%% BibTeX-bib-file{ %%% filename = "groups.bib", %%% version = "1.0e", %%% date = "1999/10/20", %%% time = "18:34:33 EST", %%% checksum = "01885 1153 4292 32016" %%% author = "Greg Gamble", %%% address = "Centre for Discrete Mathematics & Computing, %%% Department of Computer Science %%% & Electrical Engineering, %%% The University of Queensland, %%% Queensland 4072, %%% Australia", %%% telephone = "+61 7 336 52425", %%% FAX = "+61 7 336 54999", %%% copyright = "Copyright (C) 1998,1999 Greg Gamble, %%% all rights reserved. Copying of this file is %%% authorised only if either: %%% (1) you make absolutely no changes to your copy, %%% including name; OR %%% (2) if you do make changes, you first rename it %%% to some other name. %%% This file may be distributed under the terms of %%% the LaTeX Project Public License, as described %%% in lppl.txt in the base LaTeX distribution.", %%% keywords = "bibtex, bibliography, latex", %%% supported = "yes", %%% abstract = "BibTeX .bib file containing a superset of the %%% references used in the author's PhD thesis (1996). %%% Overlaps to some extent, but with different keys, %%% with Eamonn O'Brien's algebra.bib. Keys are formed %%% by an abbreviation of the surname(s) of the author(s) %%% suffixed by the last two digits of the year and %%% an alphabetic lowercase letter if necessary. %%% Change History: %%% Version 1.0: 1998/07/14 %%% Version 1.0a: 1998/10/13 %%% Version 1.0b: 1999/02/16 %%% Version 1.0c: 1999/02/17 %%% Version 1.0d: 1999/02/27 %%% Version 1.0e: 1999/10/20" %%% docstring = "The checksum field above contains a CRC-16 %%% checksum as the first value, followed by the %%% equivalent of the standard UNIX wc (word %%% count) utility output of lines, words, and %%% characters. This is produced by Robert %%% Solovay's checksum utility.", %%% } %%% ==================================================================== @preamble{ "\providecommand{\noopsort}[1]{} " # "\providecommand{\printfirst}[2]{#1} " # "\providecommand{\singleletter}[1]{#1} " # "\providecommand{\switchargs}[2]{#2#1} " } @ARTICLE{Asch84, author = "M. Aschbacher", title = "On the maximal subgroups of finite classical groups", journal = "Invent. Math.", volume = 76, year = 1984, pages = "469-514", } @ARTICLE{Asch87, author = "M. Aschbacher", title = "Chevalley groups of type {$\mathrm{G}_2$} as the group of a trilinear form", journal = "J. Algebra", volume = 109, year = 1987, pages = "193-259", } @ARTICLE{Bab81, author = "L. Babai", title = "On the order of uniprimitive permutation groups", journal = "Ann. Math.", volume = 113, year = 1981, pages = "553-568", } @ARTICLE{Bab82, author = "L. Babai", title = "On the order of doubly transitive permutation groups", journal = "Invent. Math.", volume = 65, year = 1982, pages = "473-484", } @ARTICLE{BCP82, author = "L. Babai and P. J. Cameron and P. P. Palfy", title = "On the orders of primitive groups with restricted nonabelian composition factors", journal = "J. Algebra", volume = 79, year = 1982, pages = "161-168", } @ARTICLE{Boch89, author = "A. 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Wilson", title = "An Atlas of finite groups", publisher = "University Press", address = "Oxford", year = 1985, } @ARTICLE{Coop78, author = "Cooperstein, Bruce N.", title = "Minimal degree for a permutation representation of a classical group", journal = "Israel J. Math.", volume = 30, number = 3, year = 1978, pages = "213-235", } @ARTICLE{Coop81, author = "B. N. Cooperstein", title = "Maximal subgroups of {$\mathrm{G}_2({)2^n}$}", journal = "J. Algebra", volume = 70, year = 1981, pages = "23-36", } @BOOK{Dic58, author = "L. E. Dickson", title = "Linear groups with an exposition of the {G}alois theory", publisher = "Dover", address = "New York", year = 1958, } @BOOK{Dorn71a, author = "L. Dornhoff", title = "Group representation theory", volume = "A", publisher = "Marcel Dekker, Inc.", address = "New York", year = 1971, } @BOOK{Dorn71b, author = "L. Dornhoff", title = "Group representation theory", volume = "B", publisher = "Marcel Dekker, Inc.", address = "New York", year = 1971, } @ARTICLE{Eno70, author = "H. Enomoto", title = "Conjugacy classes of {C}hevalley groups of type $(\mathrm{G}_2)$ over finite fields of characteristic 2 or 3", journal = "J. Fac. Sci. Univ. Tokyo", volume = 16, year = 1970, pages = "497-512", } @ARTICLE{FKS81, author = "B. Fein and W. M. Kantor and M. Schacher", title = "Relative {B}rauer Groups", journal = JREIA, volume = 328, year = 1981, pages = "39-57", } @ARTICLE{GP94, author = "A. Gardiner and C. E. Praeger", title = "Transitive permutation groups with bounded movement", journal = "J. Algebra", volume = 168, year = 1994, pages = "798-803", } @PHDTHESIS{GG96, author = "Greg Gamble", title = "Elements of prime order in primitive permutation groups", type = "{PhD} Thesis", school = "University of Western Australia", year = 1996, url = "http://maths.uwa.edu.au/~gregg/GGthesis.ps", } @BOOK{Gor68, author = "Gorenstein, Daniel", title = "Finite groups", publisher = "Harper \& Row", address = "New York", year = 1968, } @ARTICLE{GorL83, author = "Gorenstein, Daniel and Lyons, Richard", title = "The local structure of finite groups of characteristic 2 type", journal = "Mem. Amer. Math. Soc.", volume = 42, number = 276, year = 1983, pages = "vii+731", } @BOOK{Gor83, author = "D. Gorenstein", title = "The classification of finite simple groups", volume = 1, publisher = "Plenum Press", address = "New York", year = 1983, } @ARTICLE{Gur83, author = "Guralnick, Robert M.", title = "Subgroups of prime power index in a simple group", journal = "J. Algebra", volume = 81, number = 2, year = 1983, pages = "304-311", } @ARTICLE{Hall54, author = "P. Hall", title = "Finiteness conditions for soluble groups", journal = "Proc. London Math. Soc. (3)", volume = 4, year = 1954, pages = "419-436", } @ARTICLE{Hart26, author = "R. W. Hartley", title = "Determination of the ternary linear collineation groups whose coefficients lie in the {$\mathrm{GF}(2^n)$}", journal = "Ann. Math.", volume = 27, year = 1926, pages = "140-158", } @ARTICLE{Her74, author = "C. Hering", title = "Transitive linear groups and linear groups which contain irreducible subgroups of prime order", journal = "Geom. Ded.", volume = 2, year = 1974, pages = "425-460", } @ARTICLE{Her85, author = "C. Hering", title = "Transitive linear groups and linear groups which contain irreducible subgroups of prime order, {II}", journal = "J. Algebra", volume = 93, year = 1985, pages = "151-164", } @ARTICLE{HT59, author = "D. R. Hughes and J. D. Thompson", title = "The {$H_p$}-problem and the structure of {$H_p$} groups", journal = "J. Math.", volume = 9, year = 1959, pages = "1094-1101", } @BOOK{Isa76, author = "I. M. Isaacs", title = "Character theory of finite groups", publisher = "Academic {P}ress", address = "New York", year = 1976, } @ARTICLE{Jor73, author = "C. Jordan", title = "Sur la limite de transitivit\'e des groupes non altern\'es", journal = "Bull. Soc. Math. France", volume = 1, year = 1873, pages = "40-71", } @ARTICLE{Jor75, author = "C. Jordan", title = "Sur la limite du degr\'e des groupes primitifs qui contiennent une substitution donn\'ee", journal = "J. f. reine angew. Math.", volume = 79, year = 1875, pages = "248-258", } @ARTICLE{Kan79, author = "W. M. Kantor", title = "Permutation representations of the finite classical groups of small degree or rank", journal = "J. Algebra", volume = 60, year = 1979, pages = "158-168", } @INCOLLECTION{Kan85, author = "W. M. Kantor", title = "Some consequences of the classification of finite simple groups", booktitle = "Finite groups -- coming of age", series = "Contemporary Math.", volume = 45, editor = "John McKay", publisher = "Amer. Math. Soc.", address = "Providence", year = 1985, pages = "159-173", } @ARTICLE{Keg61, author = "O. H. Kegel", title = "Die {N}ilpotenz der $H_p$-{G}ruppen", journal = "Math. Z.", volume = 75, year = 1961, pages = "373-376", } @PHDTHESIS{Kleid87, author = "P. B. Kleidman", title = "The subgroup structure of some finite simple groups", type = "{PhD} Thesis", school = "University of Cambridge", year = 1987, } @ARTICLE{Kleid87a, author = "P. B. Kleidman", title = "The maximal subgroups of the finite 8-dimensional orthogonal groups {$\mathrm{P}\Omega^+_8(q)$} and of their automorphism groups", journal = "J. Algebra", volume = 110, year = 1987, pages = "173-242", } @ARTICLE{Kleid88, author = "P. B. Kleidman", title = "The maximal subgroups of the {S}teinberg triality groups {${}^3\mathrm{D}_4(q)$}, and of their automorphism groups", journal = "J. Algebra", volume = 115, year = 1988, pages = "182-199", } @ARTICLE{Kleid88a, author = "P. B. Kleidman", title = "The maximal subgroups of the {C}hevalley groups {$\mathrm{G}_2(q)$}, $q$ odd, of the {R}ee groups {${}^2\mathrm{G}_2(q)$}, and of their automorphism groups", journal = "J. Algebra", volume = 117, year = 1988, pages = "30-71", } @BOOK{KL90, author = "P. B. Kleidman and M. W. Liebeck", title = "The subgroup structure of the finite classical groups", series = "London Math. Soc. Lecture Note Series", volume = 129, publisher = "Cambridge University Press", address = "London", year = 1990, } @ARTICLE{KPW89, author = "P. B. Kleidman and R. A. Parker and R. A. Wilson", title = "The maximal subgroups of the {F}ischer group {$\mathrm{F}_{23}$}", journal = "J. London Math. Soc. (2)", volume = 39, year = 1989, pages = "89-101", } @ARTICLE{KW87, author = "P. B. Kleidman and R. A. Wilson", title = "The maximal subgroups of {$\mathrm{F}_{22}$}", journal = "Math. Proc. Camb. Phil. Soc.", volume = 102, year = 1987, pages = "17-23", } @ARTICLE{KW88, author = "P. B. Kleidman and R. A. Wilson", title = "The maximal subgroups of {${\rm J}_4$}", journal = "Proc. London Math. Soc. (3)", volume = 56, year = 1988, pages = "484-510", } @ARTICLE{Kov89, author = "L. G. Kov\'acs", title = "Primitive subgroups of wreath products in product action", journal = "Proc. London Math. Soc. (3)", volume = 58, year = 1989, pages = "306-322", } @ARTICLE{LaS74, author = "V. Landazuri and G. M. Seitz", title = "On the degrees of projective representations of the finite {C}hevalley groups", journal = "J. Algebra", volume = 32, year = 1974, pages = "418-443", } @ARTICLE{LevN85, author = "V. M. Levchuk and Ya. N. Nuzhin", title = "Structure of {R}ee groups", journal = "Alg. i Logika", volume = 24, year = 1985, pages = "26-41", } @ARTICLE{LMacH72, author = "H. Liebeck and D. MacHale", title = "Groups with automorphisms inverting most elements", journal = "Math. Z.", volume = 124, year = 1972, pages = "51-63", } @ARTICLE{Lieb85, author = "M. W. Liebeck", title = "On the orders of maximal subgroups of the finite classical groups", journal = "Proc. London Math. Soc. (3)", volume = 50, year = 1985, pages = "426-446", } @ARTICLE{Lieb87, author = "M. W. Liebeck", title = "The affine permutation groups of rank three", journal = "Proc. London Math. Soc. (3)", volume = 54, number = 3, year = 1987, pages = "477-516", } @ARTICLE{LPS87, author = "M. W. Liebeck and C. E. Praeger and J. Saxl", title = "A classification of the maximal subgroups of the finite alternating and symmetric groups", journal = "J. Algebra", volume = 111, number = 2, year = 1987, pages = "365-383", } @ARTICLE{LPS88, author = "M. W. Liebeck and C. E. Praeger and J. Saxl", title = "On the {O'Nan-Scott} theorem for primitive permutation groups", journal = "J. Austral. Math. Soc. Ser. A", volume = 44, year = 1988, pages = "389-396", } @ARTICLE{LPS90, author = "M. W. Liebeck and C. E. Praeger and J. Saxl", title = "The maximal factorizations of the finite simple groups and their automorphism groups", journal = "Mem. Amer. Math. Soc.", volume = 86, number = 432, year = 1990, pages = "iv+151", } @ARTICLE{LPS96, author = "M. W. Liebeck and C. E. Praeger and J. Saxl", title = "On factorizations of almost simple groups", journal = "J. Algebra", volume = 185, number = 2, year = 1996, pages = "409-419", } @INPROCEEDINGS{LS84, author = "M. W. Liebeck and J. Saxl", title = "Some recent results on finite permutation groups", booktitle = "Proceedings of the {Rutgers Group Theory Year} 1983--1984", editor = "M. Aschbacher and others", publisher = "Cambridge University Press", address = "New York", year = 1984, pages = "53-61", } @ARTICLE{LS85, author = "M. W. Liebeck and J. Saxl", title = "Primitive permutation groups containing an element of large prime order", journal = "J.~London Math. Soc. (2)", volume = 31, number = 2, year = 1985, pages = "237-249", } @ARTICLE{LS86, author = "M. W. Liebeck and J. Saxl", title = "The finite primitive permutation groups of rank three", journal = "Bull. London Math. Soc.", volume = 18, year = 1986, pages = "165-172", } @ARTICLE{LS87, author = "M. W. Liebeck and J. Saxl", title = "On the orders of maximal subgroups of the finite exceptional groups of {L}ie type", journal = "Proc. London Math. Soc. (3)", volume = 55, year = 1987, pages = "299-330", } @ARTICLE{LS91, author = "M. W. Liebeck and J. Saxl", title = "Minimal degrees of primitive permutation groups with an application to monodromy groups of {R}iemann surfaces", journal = "Proc. London Math. Soc. (3)", volume = 63, year = 1991, pages = "266-314", } @ARTICLE{Lint89, author = "S. A. Linton", title = "The maximal subgroups of the {T}hompson group", journal = "J. London Math. Soc. (2)", volume = 39, year = 1989, pages = "79-88", } @ARTICLE{LW91, author = "S. A. Linton and R. A. Wilson", title = "The maximal subgroups of the {F}ischer groups {$\mathrm{F}_{24}$} and {$\mathrm{F}_{24}'$}", journal = "Proc. London Math. Soc. (3)", volume = 63, year = 1991, pages = "113-164", } @ARTICLE{MP96, author = "A. Mann and C. E. Praeger", title = "Transitive permutation groups of minimal movement", journal = "J. Algebra", volume = 181, year = 1996, pages = "903-911", } @ARTICLE{Man09, author = "W. A. Manning", title = "On the order of primitive groups", journal = "Trans. Amer. Math. Soc.", volume = 10, year = 1909, pages = "247-258", } @ARTICLE{Man11, author = "W. A. Manning", title = "On the limit of the degree of primitive groups", journal = "Trans. Amer. Math. 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Tchackerian", title = "The maximal subgroups of {$\mathrm{G}_2(4)$}", journal = "J. Algebra", volume = 76, year = 1982, pages = "171-185", } @ARTICLE{Praeger73, author = "C. E. Praeger", title = "Sylow subgroups of transitive permutation groups", journal = "Math. Z.", volume = 134, year = 1973, pages = "179-180", } @ARTICLE{Praeger74, author = "C. E. Praeger", title = "On the {S}ylow subgroups of a doubly transitive permutation group", journal = "Math. Z.", volume = 137, year = 1974, pages = "155-171", } @ARTICLE{Praeger75, author = "C. E. Praeger", title = "Primitive permutation groups containing an element of order $p$ of small degree, $p$ a prime", journal = "J. Algebra", volume = 34, year = 1975, pages = "540-546", } @ARTICLE{Praeger76, author = "C. E. Praeger", title = "Primitive permutation groups containing an element of order $p$ of small degree, $p$ a prime, {II}", journal = "J. Algebra", volume = 42, year = 1976, pages = "278-293", } @ARTICLE{Praeger79a, author = "C. E. 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Oxford 1967", publisher = "Pergamon", address = "London", year = 1970, pages = "169-183", } @ARTICLE{Suz60, author = "M. Suzuki", title = "A new type of simple groups of finite order", journal = "Proc. Acad. Sci. U.S.A.", volume = 46, year = 1960, pages = "868-870", } @ARTICLE{Suz62, author = "M. Suzuki", title = "On a class of doubly transitive groups", journal = "Ann. Math.", volume = 75, year = 1962, pages = "105-145", } @ARTICLE{TangW88, author = "S. W. Tang and J. Wang", title = "The primitive groups of degrees 21 to 30", journal = "Beijing Daxue Xuebao", volume = 24, number = 3, year = 1988, language = "Chinese", pages = "269-276", } @BOOK{Tay92, author = "D. E. Taylor", title = "The geometry of the classical groups", series = "Sigma Series in Mathematics", volume = 9, publisher = "Heldermann", address = "Berlin", year = 1992, } @ARTICLE{Tcha81, author = "K. B. Tchackerian", title = "The maximal subgroups of {T}its simple group", journal = "Compt. Rend. Acad. Bulg. 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