Shely Mutiara Maghfira, Nugroho Dwi Widodo, Rizky Rosjanuardi, Sumanang Muhtar Gozali
A cyclically ordered group G has cyclically ordered subgroups. There could be a subgroup that is both cyclically ordered and linear on a cyclically ordered group that is an external direct product of a linearly ordered group and a nonlinear cyclically ordered group. G is a cyclically ordered group that is the external direct product of two nonlinear cyclically ordered groups C1and C2, denoted G=C1×C2. In addition, we examine a condition for a cyclically ordered group G so that a subgroup H of G with a linear cyclic order could exists. By decomposing C1and C2 into the external direct product of a linearly ordered group and a nonlinear cyclically ordered group, the condition is met. Suppose that C1 = L1 × C1′ and C2 = L2 × C2′. We consider a subgroup H=(L1×{e′1}) × (L2×{e′2}) of G, where e′1 is an identity element in C′1 and e′1 is an identity element in C′2. For a group G = C1 × C2 where G, C1, and C2 are cyclically ordered groups that are not linear, G has a linear subgroup which the positive cone of the subgroup is a semigroup. © 2023 Author(s).
Department of Mathematics Education Fpmipa, Universitas Pendidikan Indonesia, Setiabudhi Street. 229th, Bandung, 40154, Indonesia
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