MAG,

I'm afraid I must argue THAT story with you. Where you go wrong is that the answer was not one word. It was encompassed in a number of passages, which make it clear that it is the sovereignty over men that is desired.

The two relevant passages of the most complete text, The Wedding of Sir Gawain and Dame Ragnell are lines 467-472:

I say no more, but above all things
women desire sovereignty, for that is their liking
and that is their most desire
to have the rule of the manliest men
and then are they well. Thus they me did ken   [ie teach]
to rule thee, Gromer Sir.


and lines 697-698:

and also he should give me the sovereignty
of all his body and goods, surely

(The translations from Middle English above are mine, but I used modern cognates so the changes are primarily to the spelling of words).

In the ballad version (Child 31), she is said only to want "her will," which is an ironic "trick answer" ("her will" merely means "what she wants," so the riddle becomes a tautology, "she wants what she wants.") It is often a characteristic in stories containing "neck riddles" (a riddle which you must answer or be killed) that the answer is some kind of trick.

Were you thinking of other versions of this tale, MAG?