In this paper, the concepts of nilpotent and Engel orthomodular lattices, similar with the solvable orthomodular lattices are defined and their properties are investigated. The notion of [Formula: see text]-Engel orthomodular lattices as a natural generalization of distributive orthomodular lattices is introduced, and we discuss Engel orthomodular lattices, which is defined by left and right normed commutators.
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A. Najafi (2024) studied this question.
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