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The problem of giving conditions on $(p,q,a,b)$ implying a center for the Abel equation is analogous to the classical Poincar\\'e Center-Focus problem for plane vector fields.\n  Following [3,4,8,9] we say that Abel equation has a \"parametric center\" if for each $\\varepsilon \\in \\mathbb C$ the equation $y'=p(x)y^3 + \\varepsilon q(x) y^2$ has a center. 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