[FOM] Need reference on result about polynomial equations

[joeshipman@aol.com]

Although the general quintic equation is not solvable by radicals, it 
does have a general algebraic solution in terms of functions of one 
variable (in particular, in terms of radicals of degrees 2,3, and 5 
plus the "Bring Radical" solution of x^5+x=a,which is an analytic 
function of a single variable).

I have read that this cannot be done for the sextic -- no combination 
of analytic functions of one variable solves the general sixth degree 
equation.

Can anyone give me a reference (in English, preferably online) for this 
result? And how high does the degree have to get before there is no 
general solution in terms of (analytic) functions of two variables?

-- JS