Pro-p subgroups of spin groups and quaternion algebras

The main objective of this thesis is to classify pro-p subgroups of the spin groups of
Clifford algebras defined on modules over p-adic rings using the method developed
by Richard Pink. To accomplish this, we make certain changes to the original work
which deals with pro-p subgroups of SL_2, and adapt the method to the Clifford algebra
setting. Our main results consist of three cases of Pink's method on Clifford algebras:
the Quaternion algebra (n = 2), and the Spin group of Clifford algebras with n = 3; 4.
Later, we will discuss the reasons why the method stops working when n > 4, and
a possible application on a certain Galois deformation problem in a work done by
Gebhard Bockle.