Let F be the underlying base field of characteristic p 〉 3 and denote by M the even part of the finite-dimensional simple modular Lie superalgebra M. In this paper, the generator sets of the Lie algebra M which will be heavily used to consider the derivation algebra Der（M） are given. Furthermore, the derivation algebra of M is determined by reducing derivations and a torus of M, i.e., Der（m）=ad（m） spanF{∏l ad （ξr＋1ξl）} spanF{adxi,ad（xiξ^v）∏ad（ξr＋1ξl）}. As a result, the derivation algebra of the even part of M does not equal the even part of the derivation superalgebra of M.
The main purpose of the present paper is to give some properties of the Jacobson radical, the Frattini subsystem and c-ideals of a Lie triple system. Some further results concerning the Frattini subsystems of nilpotent and solvable Lie triple systems are obtained. Moreover, we develop inititally c-ideals for a Lie triple system and make use of them to give some characterizations of a solvable Lie triple system.
