On the norm property of the Hilbert symbol for polynomial formal modules in a multidimensional local field

In a two-dimensional local field K containing the pth root of unity, a polynomial formal group F _c (X, Y) = X + Y + cXY acting on the maximal ideal M of the ring of integers б _K and a constructive Hilbert pairing {·, ·} _c : K ₂(K) × F _c (M) → <ξ> _c , where <ξ> _c is the module of roots of [p] _c (pth degree isogeny of F _c ) with respect to formal summation are considered. For the extension of two-dimensional local fields L/K, a norm map of Milnor groups Norm: K ₂(L) → K ₂(K) is considered. Its images are called norms in K ₂(L). The main finding of this study is that the norm property of pairing {·, ·}c: {x,β} _c : = 0 ? x is a norm in K ₂(K([p] _c ^-1 (β))), where [p] _c ^-1 (β) are the roots of the equation [p] _c = β, is checked constructively.