Mark L. Lewis, Alexander Moretó, Thomas R. Wolf
Non-divisibility among character degrees
In this paper, we study groups for which if 1 <
a < b are character degrees, then a does not
divide b. We say that these groups have the condition no divisibility
among degrees (NDAD). We conjecture that the number of character degrees of a
group that satisfies NDAD is bounded and we prove this for solvable groups. More
precisely, we prove that solvable groups with NDAD have at most four character
degrees and have derived length at most 3. We give a group-theoretic
characterization of the solvable groups satisfying NDAD with four character
degrees. Since the structure of groups with at most three character degrees is
known, these results describe the structure of solvable groups with
NDAD.
Journal of Group Theory, Walter de Gruyter
Print ISSN: 1433-5883
Volume: 8, 09/2005
Seiten: 561 - 588
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