Computing matrix representations
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- by Vahid Dabbaghian and John D. Dixon PDF
- Math. Comp. 79 (2010), 1801-1810 Request permission
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
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Additional Information
- Vahid Dabbaghian
- Affiliation: MoCSSy Program, The IRMACS Centre, Simon Fraser University, Burnaby, BC V5A 1S6, Canada
- Email: vdabbagh@sfu.ca
- John D. Dixon
- Affiliation: School of Mathematics and Statistics, Carleton Unversity, Ottawa, ON K1S 5B6, Canada
- Email: jdixon@math.carleton.ca
- Received by editor(s): November 12, 2008
- Received by editor(s) in revised form: July 16, 2009
- Published electronically: January 12, 2010
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 79 (2010), 1801-1810
- MSC (2010): Primary 20C40; Secondary 20C15
- DOI: https://doi.org/10.1090/S0025-5718-10-02330-6
- MathSciNet review: 2630014