On weak isometries in directed groups

Rok, strany: 2019, 989 - 998

In the paper weak isometries in directed groups are investigated. It is proved that for every weak isometry $f$ in a directed group $G$ the relation $f(UL(x, y) \cap LU(x, y)) = UL(f(x), f(y)) \cap LU(f(x), f(y))$ is valid for each $x, y \in G.$ The notions of an orthogonality of two elements and of a subgroup symmetry in directed groups are introduced and it is shown that each weak isometry in a 2-isolated directed group or in an abelian directed group is a composition of a subgroup symmetry and a right translation. It is also proved that stable weak isometries in a 2-isolated abelian directed group $G$ are directly related to subdirect decompositions of the subgroup $G₂ = \{2x; x \in G \}$ of $G.$

ISO 690:

Jasem, M. 2019. On weak isometries in directed groups. In Mathematica Slovaca, vol. 69, no.5, pp. 989-998. 0139-9918. DOI: https://doi.org/ 10.1515/ms-2017-0283

APA:

Jasem, M. (2019). On weak isometries in directed groups. Mathematica Slovaca, 69(5), 989-998. 0139-9918. DOI: https://doi.org/ 10.1515/ms-2017-0283

Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava