We broadly generalise Mermin-type arguments on GHZ states. and we provide exact group-theoretic conditions for non-locality to be achieved. Our results are of interest in quantum foundations. where they yield a new hierarchy of quantum-realisable All-vs-Nothing arguments. https://www.roneverhart.com/HP-Pavilion-15-eg1053cl-15-6-FHD-Touch-Intel-Core-i5-1235U-3-30-GHz-Intel-Iris-Xe-Graphics-12-GB-DDR4-RAM-512-GB-SSD-/