scholarly journals Permutation representation of groups with Boolean orthogonalities

1981 ◽  
Vol 30 (4) ◽  
pp. 412-418
Author(s):  
Gary Davis
Keyword(s):  
Topological Space ◽  
Finiteness Condition ◽  
Permutation Representation ◽  
Ordered Groups ◽  
Lattice Ordered Groups ◽  
Group Of Homeomorphisms

AbstractReduced rings and lattice-ordered groups are examples of groups with Boolean orthogonalities. In this note we show that any group with a Boolean orthogonality satisfying a finiteness condition introduced by Stewart is isomorphic with a group of homeomorphisms of a topological space, in which two homeomorphisms are orthogonal if and only if they have disjoint supports.

Generalized Commutativity of Lattice-Ordered Groups

2015 ◽  
Vol 65 (2) ◽  
Author(s):  
M. R. Darnel ◽  
W. C. Holland ◽  
H. Pajoohesh
Keyword(s):  
Theorem Proving ◽  
Natural Generalization ◽  
Ordered Groups ◽  
Lattice Ordered Groups ◽  
Weak Commutativity

AbstractIn this paper we explore generalizations of Neumann’s theorem proving that weak commutativity in ordered groups actually implies the group is abelian. We show that a natural generalization of Neumann’s weak commutativity holds for certain Scrimger ℓ-groups.

A theorem and a question about epicomplete archimedean lattice-ordered groups

2009 ◽  
Vol 62 (2-3) ◽  
pp. 165-184 ◽  
Author(s):  
R. N. Ball ◽  
A. W. Hager ◽  
D. G. Johnson ◽  
A. Kizanis
Keyword(s):  
Ordered Groups ◽  
Lattice Ordered Groups ◽  
Archimedean Lattice

Suprema of classes of generalized scrimger varieties of lattice ordered groups

1981 ◽  
Vol 176 (3) ◽  
pp. 293-309 ◽  
Author(s):  
Norman R. Reilly ◽  
Roger Wroblewski
Keyword(s):  
Ordered Groups ◽  
Lattice Ordered Groups
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