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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2022, Number 12, Pages 101–112
DOI: https://doi.org/10.26907/0021-3446-2022-12-101-112 (Mi ivm9841) 		 
The Markoff theory and the commutator subgroup $SL(2,Z)'$

Paul Schmutz Schaller

Switzerland
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DOI: https://doi.org/10.26907/0021-3446-2022-12-101-112
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.
Received: 02.03.2022
Revised: 02.03.2022
Accepted: 29.06.2022
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2022, Volume 66, Issue 12, Pages 91–101
DOI: https://doi.org/10.3103/S1066369X22120106
Document Type: Article
UDC: 517
Language: Russian
Citation: Paul Schmutz Schaller, “The Markoff theory and the commutator subgroup $SL(2,Z)'$”, Izv. Vyssh. Uchebn. Zaved. Mat., 2022, no. 12, 101–112; Russian Math. (Iz. VUZ), 66:12 (2022), 91–101
Citation in format AMSBIB
\Bibitem{Sch22}
\by Paul~Schmutz~Schaller
\paper The Markoff theory and the commutator subgroup $SL(2,Z)'$
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2022
\issue 12
\pages 101--112
\mathnet{http://mi.mathnet.ru/ivm9841}
\crossref{https://doi.org/10.26907/0021-3446-2022-12-101-112}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2022
\vol 66
\issue 12
\pages 91--101
\crossref{https://doi.org/10.3103/S1066369X22120106}
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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