Abstract: We extended c-supplemented subalgebras, E-algebras and Frattini theory of Lie superalgebras and Lie supertriple systems for δ-Lie supertriple systems, obtained some important properties and gave a necessary condition for solvable δ-Lie supertriple systems. Moreover, we gave a necessary and sufficient condition for the judgement of c-supplemented δ-Lie supertriple systems and E-δ-Lie supertriple systems, respectively.

Key words: δ-Lie supertriple system, c-supplemented δ-Lie supertriple system, E-δ-Lie supertriple system, Frattini subsystem