@misc{10498/40410,
year = {2026},
month = {4},
url = {http://hdl.handle.net/10498/40410},
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.},
publisher = {American Mathematical Society},
keywords = {topological group},
keywords = {ordered group},
keywords = {order topology},
title = {Generalized topological ordered groups},
doi = {10.3934/ERA.2026147},
author = {García Pacheco, Francisco Javier and Moreno Frías, María Ángeles and Rahbariyan, Sakineh},
}