Groups in which the Commutator Operation Satisfies Certain Algebraic Conditions

Denote the commutator of two group elements a and b by

aba^-1b^-1=(a,b)                                                               (1)

then the associative law for the commutator operation is

 (a, b), c) = (a, (b,c)).                                                    (2)

If (2) is satisfied for every triplet of elements of a group, this group will be called an S group. If (2) is supposed to be satisfied whenever two of the elements a, b, c are equal (alternating law), then the group will be called an L-group.