The purpose of this work is to show the following result: Theorem: Let \(B\) be a CW-complex and denote by \(X\) the loops on \(B\), \(\Omega B\). If \(H_*(X)=\bigoplus _i H_i(X)\) is a finitely generated abelian group, then \(X\) is homotopy equivalent to a compact, smooth parallelizable manifold. Basically from section 2 of the paper we have: The problem in question first is reduced to the case where the fundamental group of \(X\) is finite. Then one considers the case where the dimension of \(X\) is \(\geq 5\) (so one can use surgery) and the low dimension case which is treated by special arguments. The method of proof is to construct orientable fibrations \(S^1\to X \to Y\) satisfying certain conditions, which are suitable to use surgery. The construction of such fibrations uses localization and the theory of \(p\)-compact groups where the work of \textit{T. Bauer} [Topology 43, 569--597 (2004; Zbl 1052.55019)] is crucial. The above approach takes care of the general case but with few exceptions which correspond to the spaces having rational types of the form \((3^k,7^{\varepsilon})\), \(\varepsilon=0,1\). These cases are treated by a special argument. A good brief introduction of the problem is given in the introduction. Several of previous works of the authors are used.