Abstract
We use the free entropy dened by D. Voiculescu to prove that the free group factors cannot be decomposed as closed linear spans of noncommutative monomials in elements of nonprime subfactors or abelian -subalgebras, if the degrees of monomials have an upper bound depending on the number of generators. The resulting estimates for the hypernite and abelian dimensions of free group factors settle in the armative a conjecture of L. Ge and S. Popa (for innitely many generators).
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