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?

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 DOI: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 DOI: 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. 


Sidney Garrison wrote a 1973 dissertation directed by Marty Isaacs at Wisconsin: On Groups with a Small Number of Character Degrees. There is a related paper MR0407120 (53 #10903) 20C15, Garrison, Sidney C., Bounding the structure constants of a group in terms of its number of irreducible character degrees. J. Algebra 32 (1974), no. 3, 623–628. For a solvable group, Fitting length is shown to be bounded by the number of irreducible character degrees. Then four unrelated papers through 1986, the last with S. Gagola at Kent State (by then Garrison was apparently unaffiliated). This much I get from MathSciNet, but Marty Isaacs could fill in more details. 

