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Character Degrees and Derived Length of a Solvable Group

Published online by Cambridge University Press:  20 November 2018

I. M. Isaacs
I. M. Isaacs*
Affiliation:
University of Wisconsin, Madison, Wisconsin
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Let G be a finite group. (All groups considered here are finite). There exist several results which control the structure of G in terms of cd(G), the set of degrees of the irreducible complex characters of G. Here, we are concerned with the situation where only the cardinality of cd(G) is given. If |cd(G)| ≦ 3,, then it is known [9 ; 7] that G is solvable and the derived length dl (G) ≦ cd (G) |., If |cd(G)| = 4, then G need not be solvable (e.g., G = PSL(2, 2n))\ however [5], if G is solvable then dl(G) ≦4.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 1 , 01 February 1975 , pp. 146 - 151
Copyright
Copyright © Canadian Mathematical Society 1975

References

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