%0 Journal Article %T Study of an identity %A Patrick Dehornoy %J Mathematics %D 2001 %I arXiv %X We solve the word problem of the identity $x(yz) = (xy)(yz)$ by investigating a certain group describing the geometry of that identity. We also construct a concrete realization of the free system of rank~1 relative to the above identity %U http://arxiv.org/abs/math/0111158v1