Friend Associative Quasigroup

When your social life fails to satisfy the most basic algebraic properties. A quasigroup is a mathematical structure where you can combine elements, but it lacks an identity element (that one friend who's always there) and associativity (where the order of hanging out matters). So basically, you've got friends you can hang out with, but there's no "default friend" to fall back on, and whether you hang with Alice then Bob or Bob then Alice produces completely different social dynamics. It's like having a group chat where everyone shows up but nobody actually coordinates anything. The mathematical equivalent of "we should totally hang out sometime" that never materializes into a concrete plan.