When in a 3-net the three line pencils are permuted, then with some additional requirements the net is mapped onto itself in a way which also induces a map of a coordinatizing loop (Q*), onto another, “isostrophic” loop (Q*, O). Every identity ab = aOb induces a net collineation and, simultaneously, a loop law. This procedure is used for finding collineations of a translation plane such that their existence is a necessary and sufficient condition for the validity of some laws in the multiplicative loop of a coordinatizing quasifield. Proofs can be found in [1, 2, 3].