Reference request: A theorem by S. Garrison 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: 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.
A: 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.    
