Finite Groups with Irreducible Projective Representations of Large Degree

Abstract

In this article, we will investigate finite groups G that possess a 2-cocycle for which all the complex irreducible projective representations have the same degree. We will show that, provided the number of such inequivalent irreducible projective representations is relatively small compared to the order of G, then the degree equality property is inherited by all the Sylow subgroups of G.

Key Words:

• Projective representation
• Schur multiplier

2000 Mathematics Subject Classification:

• Primary 20C25

ACKNOWLEDGMENTS

The author would like to thank the staff of the Department of Mathematics, University of Otago, New Zealand for the support they offered me during my sabbatical stay in 2009, during which this paper was written. The author would also like to thank the referee for making a number of sensible suggestions. Adoption of those suggestions has substantially improved this article.

Notes

Communicated by D. Macpherson.