The commutator and solvability in a generalized orthomodular lattice
Edwin Marsden · Pacific Journal of Mathematics · 1970
In this paper we prove in a generalized orthomodular lattice the analog of the following theorem from group theory.For a and b members of a group G, let abar 1 ^1 be the commutator of a and b.The set of commutators in G generates a normal subgroup H of G possessing these properties: G/H is Abelian.Moreover, if K is any normal subgroup of G for which G/K is Abelian, then K 2 H. Continuing the analogy with group theory, we determine a solvability condition on generalized orthomodular lattices.