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We discuss the relation between angular momenta and masses of galaxy structures base on the Li model of the universe with global rotation. In our previous paper  it was shown that the model predicts the presence of a minimum in this relation. In the present paper we discuss observational evidence allowing us to verify this relation. We find null angular momentum J = 0 for the masses corresponding to the groups mass of the galaxy, and non-vanishing angular momenta for other galactic structures. We check these theoretical predictions analysing Tully's galaxy groups. The existing data comparing alignment in different galactic structures are consistent with the obtained theoretical relation J(M) if we interpret the growing alignment as the galactic increasing angular momenta in the galactic structure.