ISIS is Islam. Why? They follow the words of the Koran and Hadiths for violence. The Koran violence can be seen here: http://www.thereligionofpeace.com/quran/023-violence.htm.
Many Muslims say that the violence is interpreted incorrectly. They say that Islam is a religion of peace. The peace is only for Muslims. Look at the words in the link. Are they interpret incorrectly? No. They are words of violence which are correctly translated.
Islamic clerics have taught Muslims that the words in the Koran do not say what they say. But anybody can see that the words are the accurately translated. What is the result of all this? Most Muslims are really not Muslim, because they believe the clerics rather than the Koran. This is why ISIS kills many of them. ISIS is killing backsliders who will not join them and obey the Koran.
Are you Muslim? Obey the Koran and kill people who are not Muslim. That is what the Koran says. That is what ISIS is doing.
Yes. So, when ISIS kills other Muslims, they are only obeying the instructions in the Koran... to kill people who are falling away from Islam. This force makes Islam to be government besides religion.
My hope is that peaceful Muslims would unite, throw off Islam, and form a true religion of peace, but kill off violent Islam followers as their right of defense. And, that they would do this formally. There are many religions of peace all over the world that Muslims could copy to do this.