Cubic formula

matt grime

That is solvable/soluble: G is soluble if there exists a chain of NORMAL (enphasis because I can't remember the tex for the normal symbol) subgroups:

[tex]1=G_0 < G_1 < .... G_n = G[/tex] and each quotient [tex]G_i/G_{i-1}[/tex] is abelian. It is certainly not necessary that the quotients are "essentially unique"

HallsofIvy

Matt: I much prefer "sovable". Whenever I see not "soluble", I immediately think "not even if you put in strong acid?"

matt grime

I agree, but Ian Stewart, whose book is the preferred teaching material for galois theory these days in many places, uses soluble.