Upper bound for the order of the normal closure [closed]

Let L|F be a finite field extension. Is it true that, if K is the normal closure of L (in some algebraic closure), then [K:F]<=[L:F]!

I think it is true. Anyone knows a proof or where to find one?

flag	asked Sep 15 2011 at 6:52 Eugenio 1

	Please try the site math.stackeschange.com which has a broader scope than MO, which is primarily for research-level mathematics questions. – David Roberts Sep 15 2011 at 7:15
	Thanks. I wasn't lucky searching in other forums, but I didn't knew stackexchange. I'll try there. – Eugenio Sep 15 2011 at 7:20