RT journal article
T1 Generalized topological ordered groups
A1 García Pacheco, Francisco Javier
A1 Moreno Frías, María Ángeles
A1 Rahbariyan, Sakineh
A2 Matemáticas
K1 topological group
K1 ordered group
K1 order topology
AB 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.
PB American Mathematical Society
SN 2688-1594
YR 2026
FD 2026-04-15
LK http://hdl.handle.net/10498/40410
UL http://hdl.handle.net/10498/40410
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 15-nov-2026