Vol. 33, No. 2, 1970

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The commutator and solvability in a generalized orthomodular lattice

Edwin Leroy Marsden, Jr.

Vol. 33 (1970), No. 2, 357–361

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 aba1b1 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 H. Continuing the analogy with group theory, we determine a solvability condition on generalized orthomodular lattices.

Mathematical Subject Classification
Primary: 06.40
Received: 27 November 1968
Published: 1 May 1970
Edwin Leroy Marsden, Jr.