Abstract:
The commutator subgroup $SL(2,Z)'$ plays a particular role in the Markoff theory since every Markoff number is $1/3$ of the trace of same elements of $SL(2,Z)'$. The latter is a free group with two generators. We give an exhaustive description of the possible pairs of generators of $SL(2,Z)'$, including important new results.
Keywords:commutator subgroup, special linear group, Markoff number, Markoff triple, $3$-matrix.