Is there a country with more than 70% of the population of Islam without terrorist groups?
Forget 70%. There is not a single country where Muslims are more than 30% of the population, which is not having Islamic terror groups. Even in Thailand and Myanmar, where the Muslim population is only around 5%, we have Islamic terror groups.
This is true. No doubt, only a minority who choose to act in such a way. Even so, thats a huge problem.
Quran (8:39) - "And fight with them until there is no more fitna (disorder, unbelief) and religion is all for Allah"
I also hearded about a verse that say to stay peaceful when in minority, then, exterminate the enemy when in majority.
(I couldn't find this verse, so i don't know if it really says that.)