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

arXiv Mathematics eprints
 Pub Date:
 January 1997
 DOI:
 10.48550/arXiv.math/9702233
 arXiv:
 arXiv:math/9702233
 Bibcode:
 1997math......2233I
 Keywords:

 Mathematics  Group Theory