|
|||||
|
|
|
|
|
|
|
|
|
The commutator and
solvability in a generalized orthomodular lattice
Edwin Leroy Marsden, Jr. |
|
Vol. 33 (1970), No. 2, 357–361
|
Abstract |
|
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 aba−1b−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 ⊇ H. Continuing the analogy with group theory, we determine a solvability condition on generalized orthomodular lattices. |
Mathematical Subject Classification
Primary: 06.40
|
Milestones
Received: 27 November 1968
Published: 1 May 1970
|
Authors |
| Edwin Leroy Marsden, Jr. | |
|
