Survey and Additional Properties on the Transcendence Order over Q(p) in C-p

The paper is aimed at recalling the notion of transcendence order over Q(p) and its main properties. Proofs are more detailed than in the paper published in Journal of Number Theory. The main results: the order always is >= 1 and we construct a number b that is of order 1 + is an element of for every is an element of > 0. If a is of order <= t and if b is transcendental over Q(p) but algebraic over Q(p)(a), then b is of order <= t too. Finally, numbers of infinite order are constructed.