On n-dimensionally orderer groups
Notions of n-ordered and n-cyclically orderedgroups are introduced which are generalizations of well-known definitions of linearly and cyclically ordered groups. Examples of norderedand n-cyclically ordered groups are considered and some of their properties are investigated. Every locally finite n-orderedgroup with a nontrivial order is n-cyclically ordered. The group of roots of unity is the maximal locally finite two-orderable groupwith non-trivial order.
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Authors
| Name | Organization | |
| Zabarina A.I. | Tomsk State Pedagogical University | |
| Pestov G.G. | Tomsk State University | pestov@mail.tomsknet.ru |
References
Sperner E. Die Ordnungfunktionen einer Geometrie // Arch. Math. 1948. В.1. S. 9-12; 1949. В.121. S. 107-130.
Novoa L.G. On n-ordered sets and order completeness // Pacific J. Math. 1965. V.15. No. 4. P. 1337-1345.
Fuch L. Partially Ordered Algebraic Systems: Pergamon Press, 1963.
Кокорин А.И., Копытов В.М. Линейно упорядоченные группы. М.: Наука, 1984.
Пестов Г.Г. n-упорядоченные множества // Труды Иркут. гос. ун-та. 1970. Т. 74. Вып. 6.
Забарина А.И., Пестов Г.Г. К теореме Сверчковского // Сиб. мат. журн. 1984. Т. 25. № 4. С. 46-53.
Терре А.И. Элементы геометрии n-мерного порядка. - Томск, 1982, № 5941-82 Деп.
