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Groups with Relatively Few Non-Linear Irreducible Characters

Published online by Cambridge University Press:  20 November 2018

I. M. Isaacs  and
D. S. Passman
I. M. Isaacs
Affiliation:
University of Chicago, Chicago, Illinois
D. S. Passman
Affiliation:
Yale University, New Haven, Connecticut
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In (4), Seitz characterized those finite groups which have exactly one non-linear irreducible character (over the complex numbers). In this paper we are concerned with the general question of what can be deduced about a finite group G if the number of its non-linear irreducible characters m(G) is given. In particular, does the assumption that m(G) is in some sense small when compared with the order |G| impose any restrictions on the structure of G?

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 1451 - 1458
Copyright
Copyright © Canadian Mathematical Society 1968

References

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3. Landau, E., Uber die Klassenzahl der bindren quadratischen Formen von negativer Discriminante, Math. Ann. 56 (1903), 671–676.Google Scholar
4. Seitz, G., Finite groups having only one irreducible representation of degree greater than one, Proc. Amer. Math. Soc. 19 (1968), 459–461.Google Scholar