Some subsystems of a lie triple system closely related to its Frattini subsystem

Abstract

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 initially c-ideals for a Lie triple system and make use of them to give some characterizations of a solvable Lie triple system.

Keywords

Frattini subsystem / Jacobson radical / c-ideals / Solvable / Nilpotent

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