IRREDUCIBLE CHARACTER DEGREES AND NORMAL SUBGROUPS 
by I. M. Isaacs and Greg Knutson 

KEYWORDS 
        derived length, character degree, fitting subgroup 
DATE 
        February 1997 
STATUS 
        Submitted to Journal of Algebra 
COMMENT 



Abstract

Let N be a normal subgroup of a finite group G and consider the set cd(G|N) 
of degrees of irreducible characters of G whose kernels do not contain N. 
A number of theorems are proved relating the set cd(G|N) to the structure 
of N. For example, if N is solvable, its derived length is bounded above by 
a function of |cd(G|N)|. Also, if |cd(G|N)| is at most 2, then N is solvable 
and its derived length is at most |cd(G|N)|. If G is solvable and 
|cd(G|N)| = 3, then the derived length of N is at most 3.