On the power maps, orders and exponentiality of p-adic algebraic groups.

In this paper we study the question of surjectivity of the power maps g ↦ gn on p-adic algebraic groups. We give a complete solution of this question in terms of the orders of certain compact analytic subgroups. We next study the p-adic one parameter subgroups of p-adic algebraic groups and find conditions, when the union of all such one parameter groups fills up the entire group. We show that there is a close relation between the above two problems. We also obtain similar results on groups defined over rational numbers. [ABSTRACT FROM AUTHOR]