What is it about?
In the paper some important properties of weak isometries in directed groups are investigated and the notion of orthogonality of two elements in directed groups is introduced. It is shown that besides right translations, another basic type of weak isometries in directed groups are subgroups symmetries, and it is proved 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. Further it is shown that there exists a relation between stable weak isometries in 2-isolated abelian groups and the internal structure of these groups.
Featured Image
Why is it important?
Metrics preserving mappings play an important role in the theory of mathematical structures with metrics.
Read the Original
This page is a summary of: On weak isometries in directed groups, Mathematica Slovaca, October 2019, De Gruyter,
DOI: 10.1515/ms-2017-0283.
You can read the full text:
Contributors
The following have contributed to this page