Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Computing matrix representations

Authors: Vahid Dabbaghian and John D. Dixon
Journal: Math. Comp. 79 (2010), 1801-1810
MSC (2010): Primary 20C40; Secondary 20C15
Published electronically: January 12, 2010
MathSciNet review: 2630014
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ G$ be a finite group and $ \chi $ a faithful irreducible character for $ G$. Earlier papers by the first author describe techniques for computing a matrix representation for $ G$ which affords $ \chi $ whenever the degree $ \chi (1)$ is less than $ 32$. In the present paper we introduce a new, fast method which can be applied in the important case where $ G$ is perfect and the socle $ soc(G/Z(G))$ of $ G$ over its centre is abelian. In particular, this enables us to extend the general construction of representations to all cases where $ \chi (1)\leq 100$. The improved algorithms have been implemented in the new version 3.0.1 of the GAP package REPSN by the first author.

References [Enhancements On Off] (What's this?)

  • 1. M. Clausen, A direct proof of Minkwitz's extension theorem, Appl. Algebra Engrg. Comm. Comput., 8 (1997) 305-306. MR 1464791
  • 2. J. H. Conway et al., Atlas of Finite Groups, Clarendon Press, Oxford, 1985. MR 827219 (88g:20025)
  • 3. C.W. Cu rtis and I. Reiner, Representation Theory of Finite Groups and Associative Algebras, Interscience-Wiley, 1962. MR 1013113 (90g:16001)
  • 4. V. Dabbaghian, REPSN--for constructing representations of finite groups, GAP package, Version 3.0.1, (2008). ( ).
  • 5. V. Dabbaghian-Abdoly, An Algorithm to Construct Representations of Finite Groups, Ph.D. thesis, Carleton University, May 2003.
  • 6. V. Dabbaghian-Abdoly, An algorithm for constructing representations of finite groups, J. Symbolic Comput., 39 (2005) 671-688. MR 2168613 (2006e:20028)
  • 7. V. Dabbaghian-Abdoly, Constructing representations of higher degrees of finite simple groups and covers, Math. Comp., 76 (2007) 1661-1668. MR 2299793 (2007m:20019)
  • 8. J. D. Dixon, Constructing representations of finite groups , DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 11, Amer. Math. Soc., Providence, RI (1993), 105-112. MR 1235797 (94h:20011)
  • 9. The GAP Group, GAP--Groups, Algorithms, and Programming , Version 4.4.12 (2008). ( ).
  • 10. D. F. Holt and W. Plesken, Perfect Groups, Clarendon Press. Oxford, 1989. MR 1025760 (91c:20029)
  • 11. I. M. Isaacs, Character Theory of Finite Groups, Academic Press, New York, 1976. MR 0460423 (57:417)
  • 12. T. Minkwitz, Extensions of irreducible representations, Appl. Algebra Engrg. Comm. Comput., 7 (1996) 391-399. MR 1465078 (98d:20006)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 20C40, 20C15

Retrieve articles in all journals with MSC (2010): 20C40, 20C15

Additional Information

Vahid Dabbaghian
Affiliation: MoCSSy Program, The IRMACS Centre, Simon Fraser University, Burnaby, BC V5A 1S6, Canada

John D. Dixon
Affiliation: School of Mathematics and Statistics, Carleton Unversity, Ottawa, ON K1S 5B6, Canada

Received by editor(s): November 12, 2008
Received by editor(s) in revised form: July 16, 2009
Published electronically: January 12, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society