Two Generator Subsystems of Lie Triple System

Abstract

For a Lie triple system $T$ over a field of characteristic zero, some sufficient conditions for $T$ to be two-generated are proved. We also discuss to what extent the two-generated subsystems determine the structure of the system $T$. One of the main results is that $T$ is solvable if and only if every two elements generates a solvable subsystem. In fact, we give an explicit two-generated law for the two-generated subsystems.