A theorem by S. Garrison states that if $G$ is a finite solvable group and $|cd(G)| = 4$ then $dl(G)\leq |cd(G)|$ (the Taketa inequality, which is conjectured to hold for all finite solvable groups). So far I have been unable to find a proof of this theorem anywhere. The only references I have seen are to Isaacs' book on character theory (where he only mentions that it has been proven by S. Garrison), and to the Ph.d thesis of S. Garrison (which has not been published, so not much help there). oes anyone know where one might find the proof?



Reference request: A theorem by S. Garrison
A new proof was published in:


Isaacs, I. M.; Knutson, Greg. "Irreducible character degrees and normal subgroups."
J. Algebra 199 (1998), no. 1, 302–326.
[MR1489366](http://www.ams.org/mathscinet-getitem?mr=1489366)
[DOI:10.1006/jabr.1997.7191](http://dx.doi.org/10.1006/jabr.1997.7191)


This was extended to cd(G)=5 in:


Lewis, Mark L. "Derived lengths of solvable groups having five irreducible character degrees. I."
Algebr. Represent. Theory 4 (2001), no. 5, 469–489.
[MR1870501](http://www.ams.org/mathscinet-getitem?mr=1870501)
[DOI: 10.1023/A:1012706718244](http://dx.doi.org/10.1023/A:1012706718244)


It mentions that "Because of the length and complexity of his argument, Garrison never published this result." and has some other useful comments.


