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

DOI:
https://doi.org/10.1090/S0025-5718-07-01969-2

Published electronically:
January 25, 2007

MathSciNet review:
2299793

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

**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, (http://web.mat.bham.ac.uk/atlas/v2.0/).**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, (`http://www.gap-system.org/Packages/repsn.html`

).**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), (`http://www.gap-system.org`

).**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*, 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 -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*, 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)**

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Additional Information

**Vahid Dabbaghian-Abdoly**

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

Email:
vdabbagh@cecm.sfu.ca

DOI:
https://doi.org/10.1090/S0025-5718-07-01969-2

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.