I am currently working on something related to the character theory of the group of unipotent upper triangular matrices with elements in a finite field. I have seen in many papers on the topic the statement that determining the irreducible characters and conjugacy classes of these groups is a "wild" problem, but never with a proof or any additional information as to what this might mean. I have asked the professor that I am working with, and he didn't know the precise statement of this property either, only that it meant that it was impossible to solve (in some sense).
Seeing as how I have been unable to find any information about this on the internet, I am wondering if anyone could either explain it to me, or point me to a useful source. Thanks!
Here is an example paper that shows what I am talking about: http://www-stat.stanford.edu/~cgates/PERSI/papers/PatternGroups_1.pdf