Results 281 to 290 of about 1,425,221 (328)

Right-Ordered Groups

Canadian Journal of Mathematics, 1972
A group G is right-ordered if it can be totally ordered so that for any a, b, c in G, a < b implies that ac < bc. Right-ordered groups, considered as order preserving automorphisms of ordered sets, were studied by Cohn in [4]; but the first
openaire   +2 more sources

DIAGRAM GROUPS, BRAID GROUPS, AND ORDERABILITY

Journal of Knot Theory and Its Ramifications, 2003
We prove that all diagram groups (in the sense of Guba and Sapir) are left-orderable. The proof is in two steps: firstly, it is proved that all diagram groups inject in a certain braid group on infinitely many strings, and secondly, this group is then shown to be left-orderable.
openaire   +2 more sources

Atomless Lattice-Ordered Groups

Canadian Mathematical Bulletin, 1994
AbstractWe show the existence of atomless lattice-ordered groups which have doubly transitive representations. In so doing, we answer a question of M. Giraudet from 1981 [4].
openaire   +1 more source

Order-automorphism groups of Archimedean ordered groups

Canadian Mathematical Bulletin
AbstractThe group of order-preserving automorphisms of a finitely generated Archimedean ordered group of rank $2$ is either infinite cyclic or trivial according as the ratio in $\mathbb {R}$ of the generators of the subgroup is or is not quadratic over $\mathbb {Q}.$ In the case of an Archimedean ordered group of rank $2$ that is not finitely ...
openaire   +2 more sources

Home - About - Disclaimer - Privacy