Advanced search
Publication Cover
Communications in Algebra Volume 39, 2011 - Issue 10
Submit an article Journal homepage
362
Views
18
CrossRef citations to date
0
Altmetric
Original Articles

The Primitive Permutation Groups of Degree Less Than 4096

Hannah J. Coutts School of Mathematics and Statistics, University of St. Andrews, Fife, Scotland, UKCorrespondence[email protected]
,
Martyn Quick School of Mathematics and Statistics, University of St. Andrews, Fife, Scotland, UK
&
Colva M. Roney-Dougal School of Mathematics and Statistics, University of St. Andrews, Fife, Scotland, UK
Pages 3526-3546 | Received 02 Nov 2009, Published online: 14 Oct 2011

REFERENCES

  • Aschbacher , M. ( 1984 ). On the maximal subgroups of the finite classical groups . Invent. Math. 76 ( 3 ): 469 – 514 .
  • Bennett , E. R. ( 1912 ). Primitive groups with a determination of the primitive groups of degree 20 . Amer. J. Math. 34 ( 1 ): 1 – 20 .
  • Bray , J. N. , Holt , D. F. , Roney-Dougal , C. M. The Maximal Subgroups of the Low-Dimensional Finite Classical Groups. London Math. Soc. Lecture Notes. Cambridge Univeristy Press. To appear.
  • Bosma , W. , Cannon , J. , Playoust , C. ( 1997 ). The Magma algebra system. I. The user language . J. Symbolic Comput. 24 ( 3–4 ): 235 – 265 .
  • Cole , F. N. ( 1893 ). The transitive substitution-groups of nine letters . Bull. Amer. Math. Soc. 2 ( 10 ): 250 – 259 .
  • Conway , J. H. , Curtis , R. T. , Norton , S. P. , Parker , R. A. , Wilson , R. A. ( 1985 ). Atlas of Finite Groups . Oxford : Oxford University Press .
  • Dixon , J. D. , Mortimer , B. ( 1988 ). The primitive permutation groups of degree less than 1000 . Math. Proc. Cambridge Philos. Soc. 103 ( 2 ): 213 – 238 .
  • Dixon , J. D. , Mortimer , B. ( 1996 ). Permutation Groups . Graduate Texts in Mathematics. Vol. 163 . New York : Springer-Verlag .
  • Eick , B. , Höfling , B. ( 2003 ). The solvable primitive permutation groups of degree at most 6560 . London Math. Soc. J. Comput. Math. 6 : 29 – 39 .
  • The GAP Group. ( 2007 ). GAP – Groups, Algorithms, and Programming, Version 4.4.10 .
  • Hiss , G. , Malle , G. ( 2001/2002 ). Low-dimensional representations of quasi-simple groups . London Math. Soc. J. Comput. Math. 5 : 95 – 126 . Corrigenda : London Math. Soc. J. Comput. Math. 4 : 22 – 63 .
  • Holt , D. F. , Roney-Dougal , C. M. (2005). Constructing maximal subgroups of classical groups. London Math. Soc. J. Comput. Math. 8:46–79.
  • Holt , D. F. , Roney-Dougal , C. M. ( 2010 ). Constructing Maximal Subgroups of Orthogonal Groups . London Math. Soc. J. Comput. Math. 13 : 164 – 191 .
  • Huppert , B. ( 1967 ). Endliche Gruppen. I, Die Grundlehren der Mathematischen Wissenschaften, Band 134 . Berlin : Springer-Verlag .
  • Jordan , C. ( 1989 ). Traité des Substitutions et des Équations Algébriques, Les Grands Classiques Gauthier-Villars . Sceaux : Éditions Jacques Gabay. Reprint of the 1870 original .
  • Kleidman , P. , Liebeck , M. ( 1990 ). The Subgroup Structure of the Finite Classical Groups . London Math. Soc. Lecture Note Series . Vol. 129 . Cambridge : Cambridge University Press .
  • Kleidman , P. B. ( 1987 ). The maximal subgroups of the finite 8-dimensional orthogonal groups and of their automorphism groups . J. Algebra 110 ( 1 ): 173 – 242 .
  • Kleidman , P. B. , Wilson , R. A. ( 1990 ). The maximal subgroups of E6(2) and Aut(E6(2)) . Proc. London Math. Soc. (3) 60 ( 2 ): 266 – 294 .
  • Landazuri , V. , Seitz , G. M. ( 1974 ). On the minimal degrees of projective representations of the finite Chevalley groups . J. Algebra 32 : 418 – 443 .
  • Liebeck , M. W. ( 1985 ). On the orders of maximal subgroups of the finite classical groups . Proc. London Math. Soc. (3) 50 ( 3 ): 426 – 446 .
  • Liebeck , M. W. , Saxl , J. ( 1985 ). Primitive permutation groups containing an element of large prime order . J. London Math. Soc. (2) 31 ( 2 ): 237 – 249 .
  • Lübeck , F. ( 2001 ). Small degree representations of finite Chevalley groups in defining characteristic . London Math. Soc. J. Comput. Math. 4 : 135 – 169 .
  • Martin , E. N. ( 1901 ). On the imprimitive substitution groups of degree fifteen and the primitive substitution groups of degree eighteen . Amer. J. Math. 23 ( 3 ): 259 – 286 .
  • Miller , G. A. ( 1895 ). Note on the transitive substitution groups of degree twelve . Bull. Amer. Math. Soc. 1 ( 10 ): 255 – 258 .
  • Miller , G. A. ( 1896 ). List of transitive substitution groups of degree twelve . Quart. J. Pure. Appl. Math. 28 : 193 – 231 .
  • Miller , G. A. ( 1897 ). On the primitive substitution groups of degree fifteen . Proc. London Math. Soc. 28 ( 1 ): 533 – 544 .
  • Miller , G. A. ( 1897 ). Sur l’énumeration des groupes primitifs dont the degré est inférieur à 17 . C. R. Acad. Sci. 124 : 1505 – 1508 .
  • Miller , G. A. ( 1898 ). On the primitive substitution groups of degree sixteen . Amer. J. Math. 20 ( 3 ): 229 – 241 .
  • Miller , G. A. ( 1898 ). On the transitive substitution groups of degrees 13 and 14 . Quart. J. Pure. Appl. Math. 29 : 224 – 249 .
  • Miller , G. A. ( 1900 ). On the transitive substitution groups of degree seventeen . Quart. J. Pure. Appl. Math. 31 : 49 – 57 .
  • Norton , S. ( 1996 ). Improvements to the ATLAS, http:///brauer.maths.qmul. ac.uk/Atlas/info/atlasmods.dvi
  • Roney-Dougal , C. M. ( 2005 ). The primitive permutation groups of degree less than 2500 . J. Algebra 292 ( 1 ): 154 – 183 .
  • Roney-Dougal , C. M. , Unger , W. R. ( 2003 ). The affine primitive permutation groups of degree less than 1000 . J. Symbolic Comput. 35 ( 4 ): 421 – 439 .
  • Short , M. W. ( 1992 ). The Primitive Soluble Permutation Groups of Degree Less than 256 . Lecture Notes in Mathematics . Vol. 1519 . Berlin : Springer-Verlag .
  • Sims , C. C. ( 1970 ). Computational methods in the study of permutation groups . In: Computational Problems in Abstract Algebra (Proc. Conf., Oxford, 1967). Oxford : Pergamon , pp. 169 – 183 .
  • Suzuki , M. (1962). On a class of doubly transitive groups. Ann. of Math. (2) 75:105–145.
  • Theißen , H. ( 1997 ). Eine Methode zur Normalisatorberechnung in Permutations- gruppen mit Anwendungen in der Konstruktion primitiver Gruppen, PhD thesis, RWTH, Aachen, Germany .
  • Wilson , R. , Walsh , P. , Tripp , J. , Suleiman , I. , Rogers , S. , Parker , R. , Norton , S. , Nickerson , S. , Linton , S. , Bray , J. , Abbott , R. ATLAS of Finite Group Representations, http://web.mat.bham.ac.uk/atlas/v2.0/
  • Communicated by D. Macpherson.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.