galois theory tells us that that some polynomials \vskip .1in $f(x) = x^n + a_1 x^{n-1} + ... + a_{n-1} x + a_n$ \vskip .1in \noindent of degree $n > 4$ cannot be solved in radicals. equivalently, some $s_n$-covers cannot be split by a solvable base extension. j. tits asked whether an analogous assertion remains true if $s_n$ is replaced by a connected group $g$. in this talk i will discuss the background of this problem and recent results (obtained jointly with v. chernousov and $p$. gille) which indicate that solvability in radical may, indeed be possible in this setting. in particular, i will explain a connection we found between tits' question and a variant hilbert's 13th problem.