Two Generator Subsystems of Lie Triple System (Communications in Mathematical Research, 2021)
For a Lie triple system $T$ over a field of characteristic zero, some sufficientconditions for $T$ to be two-generated are proved. We also discuss to what extent thetwo-generated subsystems determine the structure of the system $T$. One of the mainresults is that $T$ is solvable if and only if every two elements generates a solvablesubsystem. In fact, we give an explicit two-generated law for the two-generatedsubsystems.
Keywords: Lie triple system; two generated subsystem; solvable.