Abstract: Among the Thompson groups, F has been known to arrive from considerations of the associative law and V has been known to arrive from considerations of the associative and commuative laws. Patrick Dehornoy has made this formal with a technique for writing down a "structure group" for any set of algebraic identities. His construction agrees with the first sentence in that his construction leads to F when the set of identities consists of the associative law and leads to V when the set of identities consists of the associative law with the commuative law. His construction allows for introduction of "braided" versions of the commutative law. We will describe what we know of Dehornoy's construction.