In this paper, we study different extensions of local fields. For an arbitrary finite extension of the field of <i>p</i>-adic numbers K/Q<sub>p</sub> it is possible to describe, using the famous Lubin-Tate theory, its maximal abelian extension K<sup>ab</sup>/K and the corresponding Galois group. It is a Cartesian product of the groups appearing from the maximal unramified extension of K and a fully ramified extension obtained using the roots of some endomorphisms of the Lubin- Tate formal groups. Here, we are going to consider so-called generalised Lubin-Tate formal groups and the extensions that appear after adding the roots of their isomorphisms to the initial field. Using the fact that for a finite unramified extension T<sub>m</sub> of degree m of the field K one of such formal groups coincides with a classical one, it became possible to obtain the Galois group of the extension (T<sub>m</sub>)<sup>ab</sup>/K. The main result of the paper is explicit description of the Galois group of the extension (K<sup>u
