I have a floating engineered wood floor in a hallway. One corner of one wood board has popped up (since there is no edge groove at that point of the board). I wonder if I should try to glue the corner of the board or use some other mean to fix it. What type of glue would you recommend?

Yes just glue it. You can use any type of construction adhesive. Liquid nail, power grab,etc.

Liquid Nail or any other type construction adhesive