@article{García-Pacheco2026, 
author = {F. J. García-Pacheco and M. A. Moreno-Frías and S. Rahbariyan},
title = {Generalized topological ordered groups},
year = {2026},
journal = {Electronic Research Archive},
volume = {34},
number = {5},
pages = {3277-3288},
keywords = {topological group, ordered group, order topology},
url = {https://www.sciopen.com/article/10.3934/era.2026147},
doi = {10.3934/era.2026147},
abstract = {A structured group is a group endowed with a binary internal relation compatible with the group operation, which can be generalized to a type of partially ordered group. In this paper, we investigated two kinds of structured groups: first, those in which the binary internal relation is an equivalence relation, where we showed that the quotient set acquires a group structure, leading to a characterization of its normal subgroups. As a consequence, we obtained that group quotients by congruencies are equivalent to group quotients by normality. Additionally, we proved that the quotient set of a topological group with a compatible equivalence relation is also a topological group whose canonical projection is an open map. The second type of structured groups, we considered, are those with a partial order relation. In this case, we identified nonrestrictive sufficient conditions for the order topology to define a monoid topology, hence, a group topology.}
}