TITLE: A set which satisfies all conditions for a Group except associativity
QUESTION [5 upvotes]: I have a question which I can't seem to prove or dismiss.
Can a set of elements A satisfy al the conditions for a group except associativity (which leaves us with closure, identity and invertibility).
Tried to prove it but can't seem to make a table which fullfiles these actions.
Thank you.

REPLY [3 votes]: Such sets are called loops, see
http://en.wikipedia.org/wiki/Loop_(mathematics)