You will receive an out-of-app-notification for all actions by users you follow or any activity within those groups in which you are a member.
To stop receiving notifications from a specific user, go to their profile and tap "Following" to unfollow them.
The opposite of this article here.
If you would like to silence a specific group without having to leave. Go to the group's settings, and toggle "Mute notifications" on.
You will no longer receive notifications until you toggle "Mute notifications" off.