Geodesic
The Markoff theory and the commutator subgroup $SL(2,Z)'$
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2022), pp. 101-112

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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
Mots-clés : Markoff triple, $3$-matrix. 
@article{IVM_2022_12_a8,
     author = {Paul Schmutz Schaller},
     title = {The {Markoff} theory and the commutator subgroup $SL(2,Z)'$},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {101--112},
     publisher = {mathdoc},
     number = {12},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2022_12_a8/}
}
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Paul Schmutz Schaller. The Markoff theory and the commutator subgroup $SL(2,Z)'$. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2022), pp. 101-112. http://geodesic.mathdoc.fr/item/IVM_2022_12_a8/