Geodesic
Convex Subgroups of Partially Right-Ordered Groups
Algebra i logika, Tome 42 (2003) no. 4, pp. 497-509.

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We study into the question of whether a partial order can be induced from a partially right-ordered group $G$ onto a space $R(G:H)$ of right cosets of $G$ w.r.t. some subgroup $H$ of $G$. Examples are constructed showing that the condition of being convex for $H$ in $G$ is insufficient for this. A necessary and sufficient condition (in terms of a subgroup $H$ and a positive cone $P$ of $G$) is specified under which an order of $G$ can be induced onto $R(G:H)$. Sufficient conditions are also given. We establish properties of the class of partially right-ordered groups $G$ for which $R(G:H)$ is partially ordered for every convex subgroup $H$, and properties of the class of groups such that $R(G:H)$ is partially ordered for every partial right order $P$ on $G$ and every subgroup $H$ that is convex under $P$.
Keywords: partially right-ordered group, convex subgroup. 
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     author = {A. M. Protopopov},
     title = {Convex {Subgroups} of {Partially} {Right-Ordered} {Groups}},
     journal = {Algebra i logika},
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     volume = {42},
     number = {4},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2003_42_4_a4/}
}
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A. M. Protopopov. Convex Subgroups of Partially Right-Ordered Groups. Algebra i logika, Tome 42 (2003) no. 4, pp. 497-509. http://geodesic.mathdoc.fr/item/AL_2003_42_4_a4/

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