A set which satisfies all conditions for a Group except associativity

group-theory

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.


Solution 1:

Hint: Take the integers under subtraction.

(Note: This is a hint, not a solution. You need to alter it slightly to get an identity, as $x-0=x$ but $0-x=-x$.)

Solution 2:

Such sets are called loops, see

http://en.wikipedia.org/wiki/Loop_(mathematics)

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