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International Journal of Applied Biology and Pharmaceutical Technology

Lie-triple-systems-innovations

As an analogue of the Frattini algebra of a Lie algebra, the Frattini subsystem of a Lie triple system is defined and some elementary properties are investigated. Some further results concerning Frattini subsystems for nilpotent Lie triple systems and solvable Lie triple systems are obtained. Moreover, some necessary and sufficient conditions for a Lie triple system to be Φ-free are given.

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