Finite Symplectic Matrix Groups

REFERENCES

• Artin , [Artin 57] E. 1957 . Geometric Algebra , New York : Interscience . Interscience Tracts in Pure and Applied Mathematics 3
   Google Scholar
• Blichfeldt , [Blichfeldt 17] H. F. 1917 . Finite Collineation Groups , Chicago : The University of Chicago Press .
   Google Scholar
• Bosma , [Bosma et al. 97] W. , Cannon , J. and Playoust , C. 1997 . “The Magma Algebra System I: The User Language.” . Journal of Symbolic Computation , 24 ( 3-4 ) : 235 – 265 .
   Web of Science ®Google Scholar
• Brown , [Brown et al. 77] H. , Bülow , R. , Neubüser , J. , Wondratschek , H. and Zassenhaus , H. 1977 . Crystallographic Groups of Four-Dimensional Space , New York : Wiley Interscience .
   Google Scholar
• Burkhardt , [Burkhardt 76] R. 1976 . “Die Zerlegungsmatrizen der Gruppen .” . Journal of Algebra , 40 : 75 – 96 .
   Web of Science ®Google Scholar
• Burnside , [Burnside 12] W. 1912 . “The Determination of All Groups of Rational Linear Substitutions of Finite Order Which Contain the Symmetric Group in the Variables.” . Proceedings of the London Mathematical Society , 2 ( 10 ) : 284 – 308 .
   Google Scholar
• Conway , [Conway et al. 85] J. H. , Curtis , R. T. , Norton , S. P. , Parker , R. A. and Wilson , R. A. 1985 . Atlas of Finite Groups , Oxford : Clarendon Press .
   Google Scholar
• Feit , [Feit 76] W. 1976 . “On Finite Linear Groups in Dimension at Most 10.” . In Proceedings of the Conference on Finite Groups (Univ. Utah, Park City, Utah, 1975) pp. 397–407.
   Google Scholar
• Feit , [Feit 82] W. 1982 . The Representation Theory of Finite Groups , Amsterdam : North-Holland .
   Google Scholar
• Hiss , [Hiss and Malle 01] G. and Malle , G. 2001 . “Low-Dimensional Representations of Quasi-simple Groups.” . LMS Journal of Computation and Mathematics , 4 : 22 – 63 . Corrigenda: 5 (2002), 95–126.
   Google Scholar
• Huppert , [Huppert 67] B. 1967 . Endliche Gruppen I , New York : Springer .
   Google Scholar
• Isaacs , [Isaacs 94] I. M. 1994 . Character Theory of Finite Groups , New York : Dover .
   Google Scholar
• Kirschmer , [Kirschmer 09] M. 2009 . “Finite Symplectic Matrix Groups.” . PhD thesis, RWTH Aachen University, Aachen. Available online (http://www.math.rwth-aachen.de/Markus.Kirschmer/symplectic/)
   Google Scholar
• Lorenz , [Lorenz 71] F. 1971 . “Über die Berechnung der Schurschen Indizes von Charakteren endlicher Gruppen.” . Journal of Number Theory , 3 : 60 – 103 .
   Google Scholar
• Minkowski , [Minkowski 87] H. 1887 . “Zur Theorie der positiven quadratischen Formen.” . Journal für die Reine und Angewandte Mathematik , 101 : 196 – 202 .
   Google Scholar
• Nebe , [Nebe 96a] G. 1996 . “Finite Subgroups of .” . Experimental Mathematics , 5 ( 3 ) : 163 – 195 .
   Google Scholar
• Nebe , [Nebe 96b] G. 1996 . “Finite Subgroups of for 25⩽n⩽31.” . Communications in Algebra , 24 ( 7 ) : 2341 – 2397 .
   Web of Science ®Google Scholar
• Nebe , [Nebe 98a] G. 1998 . “Finite Quaternionic Matrix Groups.” . Representation Theory , 2 : 106 – 223 .
   Google Scholar
• Nebe , [Nebe 98b] G. 1998 . “The Structure of Maximal Finite Primitive Matrix Groups.” . In Algorithmic Algebra and Number Theory , Edited by: Matzat , B. , Greuel , G.-M. and Hiss , G. 417 – 422 . Berlin : Springer .
   Google Scholar
• Nebe , [Nebe and Plesken 95] G. and Plesken , W. 1995 . “Finite Rational Matrix Groups.” . In Memoirs of the American Mathematical Society , Vol. 116 , Providence : AMS .
   Google Scholar
• Nebe , [Nebe et al. 01] G. , Rains , E. M. and Sloane , N. J. A. 2001 . “The Invariants of the Clifford Groups.” . Designs, Codes and Cryptography , 24 ( 1 ) : 99 – 122 .
   Google Scholar
• Plesken , [Plesken 77] W. 1977 . “On Absolutely Irreducible Representations of Orders.” . In Number Theory and Algebra , Edited by: Zassenhaus , H. New York : Academic Press . , pp. 241–262
   Google Scholar
• Plesken , [Plesken 91] W. 1991 . “Some Applications of Representation Theory.” . Progress in Mathematics , 95 : 477 – 496 .
   Google Scholar
• Reiner , [Reiner 03] I. 2003 . Maximal Orders , Oxford : Oxford Science Publications .
   Google Scholar
• Schur , [Schur 07] I. 1907 . “Über die Darstellung der endlichen Gruppen durch gebrochene lineare Substitutionen.” . Journal für die Reine und Angewandte Mathematik , 132 : 85 – 137 .
   Google Scholar
• Wall , [Wall 62] G. E. 1962 . “On the Clifford Collineation, Transform and Similarity Groups (IV).” . Nagoya Mathematical Journal , 21 : 199 – 122 .
   Google Scholar
• Winter , [Winter 72] D. L. 1972 . “The Automorphism Group of an Extraspecial p-Group.” . Rocky Mountain Journal of Mathematics , 2 ( 2 ) : 159 – 168 .
   Google Scholar