On Linear Cyclically Ordered Sub Groups of Cyclically Ordered Groups
Rizky Rosjanuardi, Isnie Yusnitha, Sumanang Muhtar Gozali

Department of Mathematics Education, FPMIPA Universitas Pendidikan Indonesia. Jl. Dr. Setia Budhi 229 Bandung-Indonesia

Abstract

Given a group G equipped with a cyclic order so that G is cyclically ordered group, in this condition, all subgroups of G are cyclically ordered. When the group G is finite the cyclic order on G is not linear, even when the group G is infinite, the cyclic order on G is not necessarily linear. In this article we discuss an infinite group G and some conditions so that there is a subgroup H of G in which the cyclic order on H is also linear. The positive cone P(H) of H is then a semigroup, meanwhile the positive cone P(G) of G is not necessarily a semigroup.

Keywords: cyclic order, group, subgroup, linear, positive cone

Topic: Mathematics