Basic definitions without equality? (Score 2, Insightful)

Group theory is the simplest sort of 'mathematical abstraction' (actually, it is a step past set theory) in that numbers and equations play no part in its basic definitions.

I thought, and Algebra by Isaacs confirms, that a group is a set G with an associative binary operation * such that there exists e in G with properties:

1. For each x in G, x*e=e*x=x.
2. For each x in G, there is a y in G such that x*y=y*x=e.

Can anyone give the definition that doesn't use equations? I didn't think so.