Regular formal modules in local fields and irregularly degree

In this paper we investigate the irregular degree of finite not ramified local field extantions with respect to a polynomial formal group and in the multiplicative case. There was found necessary and sufficient conditions for the existence of primitive roots of $p^s$ power from $1$ and (endomorphism $[p^s]F_m$) in $L$-th unramified extension of the local field $K$ (for all positive integer $s$). These conditions depend only on the ramification index of the maximal abelian subextension of the field $K$ $K_a/Q_p$.