In this paper, we prove that a free abelian group cannot occur as the group of self-homotopy equivalences of a rational CW-complex of finite type. Thus, we generalize a result due to Sullivan-Wilkerson showing that if X is a rational CW-complex of finite type such that dim H* (X, 7G) G oo or dim Tr* (X) G oo, then the group of self-homotopy equivalences of X is isomorphic to a linear algebraic group defined over Q.
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