Zilber conjectured that any simple group of finite Morley rank is isomorphic to an algebraic group over an algebraically closed field, which was formulated in Cherlin’s paper, without the finiteness of rank assumption. The conjecture now was known as the Cherlin-Zilber Conjecture or Algebraicity Conjecture. In this talk we will present several results regarding algebraicity of groups definable over the field of p-adic numbers. In the first part I will give a brief overview of the subject, and present joint work with Pillay and Jonhson on which we showed that definable f-generic groups and abelian groups are eventually algebraic. In the second part of the talk I will present a recent result which indicates that every open subgroup of an abelian algebraic group over the field of p-adic numbers is definable.