Genocide in Syria?

I believe that what is going on in Syria is not just a conflict, but is a genocide. The government is executing people, which is one of the stages of genocide. When the Arab league was trying to help the victims by creating a peace plan with Syria, Syria just kept prosecuting the people that wanted them out of power. However, it makes sense that people don't believe this is a genocide. In the definition of genocide, it says to eliminate ethnic and religious groups, along with other groups. It doesn't mention political groups. I believe this needs to be put into the definition, because I believe this is still genocide. They are still trying to wipe out a group with certain beliefs.