Bobbi Kristina -- Violent History With Nick Gordon Triggered By Jealousy

Bobbi Kristina and Nick Gordon's violent relationship was well known among their friends ... and sources tell us it was fueled by jealousy -- but not the kind you'd expect.

Sources close to the couple tell us ... their spats, which sometimes resulted in domestic violence, were almost always triggered by Nick's jealousy over Bobbi Kristina's fame. He felt he was also Whitney Houston's child since he grew up with her and could not understand why people focused on Bobbi.

One recent example ... they were trying to get their own TV show but when Nick wasn't offered the same deal as Bobbi Kristina they turned it down.

Sources close to the couple tell us Bobbi Kristina's injuries, which triggered an ongoing criminal investigation with Gordon as the target, don't surprise their friends because they've known the relationship sometimes got violent.

We made multiple attempts to reach Nick. So far, no word back.