Open AccessOn linear cyclically ordered subgroups of cyclically ordered groups
Author(s) -
Rizky Rosjanuardi,
Isnie Yusnitha,
Sumanang Muhtar Gozali
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1280/2/022044
Subject(s) - order (exchange) , semigroup , mathematics , cyclic group , group (periodic table) , combinatorics , cone (formal languages) , pure mathematics , physics , algorithm , quantum mechanics , abelian group , finance , economics
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 a semigroup.