The Markoff Theory and the Commutator Subgroup SL(2, Z)'
Paul Schmutz Schaller
Abstract
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.
Topics & Concepts
MathematicsCommutatorCommutator subgroupTRACE (psycholinguistics)Pure mathematicsGroup (periodic table)CombinatoricsDiscrete mathematicsAlgebra over a fieldNormal subgroupPhysicsLinguisticsQuantum mechanicsPhilosophyLie conformal algebraGeometric and Algebraic Topologysemigroups and automata theoryAdvanced Combinatorial Mathematics