Symbols on formal groups

The theory of a continuous Steinberg symbol in a local field is generalized to formal commutative groups. For Lubin–Tate groups, a universal symbol is constructed in explicit form, and it is shown that the module of values of an arbitrary symbol imbeds into the group of points of the formal group.
By means of this theory of symbols a new approach is given to obtaining an explicit form for the Hilbert norm residue symbol on Lubin–Tate formal groups.
Bibliography: 10 titles.