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Groups with Representations of Bounded Degree

Published online by Cambridge University Press:  20 November 2018

I. M. Isaacs  and
D. S. Passman
I. M. Isaacs
Affiliation:
Harvard University
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Let G be a discrete group with group algebra C[G] over the complex numbers C. In (5) Kaplansky essentially proves that if G has a normal abelian subgroup of finite index n, then all irreducible representations of C[G] have degree ≤n. Our main theorem is a converse of Kaplansky's result. In fact we show that if all irreducible representations of C[G] have degree ≤n, then G has an abelian subgroup of index not greater than some function of n. (The degree of a representation of C[G] for arbitrary G is defined precisely in § 3.)

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 299 - 309
Copyright
Copyright © Canadian Mathematical Society 1964

References

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