Torsion of algebraic groups and iterate extensions associated with Lubin–Tate formal groups

We show finiteness results on torsion points of commutative algebraic groups over a p-adic field K with values in various algebraic extensions L/K of infinite degree. We mainly study the following cases: (1) L is an abelian extension which is a splitting field of a crystalline character (such as a Lubin-Tate extension). (2) L is a certain iterate extension of K associated with Lubin-Tate formal groups, which is familiar with Kummer theory.