Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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



Constructing representations of higher degrees of finite simple groups and covers

Author: Vahid Dabbaghian-Abdoly
Journal: Math. Comp. 76 (2007), 1661-1668
MSC (2000): Primary 20C40; Secondary 20C15
Published electronically: January 25, 2007
MathSciNet review: 2299793
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ G$ be a finite group and $ \chi$ an irreducible character of $ G$. A simple method for constructing a representation affording $ \chi$ can be used whenever $ G$ has a subgroup $ H$ such that $ \chi_H$ has a linear constituent with multiplicity 1. In this paper we show that (with a few exceptions) if $ G$ is a simple group or a covering group of a simple group and $ \chi$ is an irreducible character of $ G$ of degree between 32 and 100, then such a subgroup exists.

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

  • 1. J.H. Conway, R.T. Curtis, S.P. Norton, R.A. Parker and R.A. Wilson, Atlas of Finite Groups. Maximal Subgroups and Ordinary Characters for Simple Groups, Claredon Press, Oxford, 1985. MR 827219 (88g:20025)
  • 2. ATLAS of Finite Group Representations, School of Mathematics and Statistics, The University of Birmingham, Version 2, (
  • 3. V. Dabbaghian-Abdoly, Constructing representations of finite simple groups and covers, Canad. J. Math., 58 (2006), 23-38. MR 2195590
  • 4. V. Dabbaghian-Abdoly, An algorithm to construct representations of finite groups, Ph.D. thesis, School of Mathematics, Carleton University, 2003.
  • 5. V. Dabbaghian-Abdoly, RPSEN - A Package for Constructing Representations of Finite Groups, GAP Package, 2004, (
  • 6. 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)
  • 7. The GAP Group, GAP--Groups, Algorithms, and Programming. Version 4.6 (2005), (
  • 8. R. Gow, Schur indices of some groups of Lie type, J. Algebra, 42 (1976), 102-120. MR 0466330 (57:6210)
  • 9. E. Güzel, Primitive idempotents of the group algebra $ \mathbb{C}{\rm SL}(3,q)$, Math. Scand., 70 (1992), no. 2, 177-185. MR 1189972 (93k:20027)
  • 10. G.J. Janusz, Primitive idempotents in group algebras, Proc. Amer. Math. Soc., 17 (1966), 520-523. MR 0194523 (33:2733)
  • 11. D. Gorenstein, R. Lyons and R. Solomon, The Classification of the Finite Simple Groups: Almost Simple $ K$-groups, Number 3., Part I., Amer. Math. Soc., Providence, RI, 1998. MR 1490581 (98j:20011)
  • 12. I.M. Isaacs, Character Theory of Finite Groups, Dover, New York, 1994. MR 1280461
  • 13. G. Karpilovsky, The Schur Multiplier, London Math. Soc. Monographs, Oxford Univ., New York, 1987. MR 1200015 (93j:20002)
  • 14. Z. Ohmori, On a Zelevinsky theorem and the Schur indices of the finite unitary groups, J. Math. Sci. Univ. Tokyo, 4 (1997), 417-433. MR 1466354 (98i:20045)
  • 15. N. Yelkenkaya, Primitive idempotents of the group algebra $ \mathbb{C}{\rm SL}(2,q)$, Istanbul Univ. Fen Fak. Mat. Derg., 55/56 (1996/97), 99-109. MR 1767540 (2001f:16051)
  • 16. A.V. Zelevinsky, Representations of Finite Classical Groups, Lecture Notes in Mathematics 869, Springer, New York, 1981. MR 643482 (83k:20017)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 20C40, 20C15

Retrieve articles in all journals with MSC (2000): 20C40, 20C15

Additional Information

Vahid Dabbaghian-Abdoly
Affiliation: The Centre for Experimental and Constructive Mathematics (CECM), Simon Fraser University, Burnaby, British Columbia, V5A 1S6, Canada

Keywords: Simple group, central cover, irreducible representation
Received by editor(s): November 27, 2005
Received by editor(s) in revised form: July 6, 2006
Published electronically: January 25, 2007
Additional Notes: This work was supported by the MITACS NCE and NSERC of Canada
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society