On norm maps and universal norms of formal groups over integer rings of local fields

We review and investigate norm maps and universal norms of formal groups over integer ring of local and quasi-local fields. Theorem on triviality of universal norm group of one dimensional fornal groups of reduction height 3 over integer ring of local and quasi-local fields is presented. The theorem on triviality of universal norm group is based on the lemma about function that gives the minimal degree of elements of the subgroup FtK of the group FK that contains the norm group NL/K (FnL). In the case of formal groups of elliptic curves the function has used by O. N. Vvedenskii and is denoted as μ(n). The proof of the lemma is also presented. © Springer International Publishing Switzerland 2014.