The aim of this paper is to study the structure of the fundamental group of a closed oriented Riemannian manifold with positive scalar curvature. To be more precise, let M be a closed oriented Riemannian manifold of dimension n (4 ≤ n ≤ 7) with positive scalar curvature and non-trivial first Betti number, and let α be a non-trivial codimension one homology class in H n−1 (M ; R). Then it is known as in [8] that there exists a closed embedded hypersurface Nα of M representing α of minimum

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... compared with all other closed hypersurfaces in the homology class. Our main result is to show that the fundamental group π 1 (Nα) is always virtually free. In particular, this gives rise to a new obstruction to the existence of a metric of positive scalar curvature.