Abstract: The variation in the irregularity degree of a finite unramified local field extensions of a local field is investigated with respect to a polynomial formal group and in the multiplicative case. The necessary and sufficient conditions for the existence of the p^sth primitive roots of the p^sth power of 1 and (endomorphism p^[s]_Fm) in the Lth unramified extension of the local field K (for all positive integers s) are found. The conditions depend only on the ramification index of the maximal Abelian subextension of the field KK_a/Q_p.