There are plenty of write-ups about this and you can read them at your own pace in the internet.
The one thing that you would probably find out for yourself after reading all the articles, is that karate and almost all forms of martial arts are constantly evolving.
Divergence from Kyokushin Karate didn’t only happen after Sosai Oyama’s death; several distinct karate groups were formed by Sosai Oyama’s students even as he was alive. Many groups bearing the banner of Kyokushin come and go. The only thing that really matters is how Kyokushin Karate can endure through the test of time and evolve to become an international sport & cultural heritage. For this, we place our trust in Shinkyokushinkai. Join us in our journey to experience the ultimate, true martial-way! Osu!