<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper, we introduce a geodesic metric space called generalized Cayley graph (gCay(P,S)) on a finitely generated polygroup. We define a hyperaction of polygroup on gCayley graph and give some properties of this hyperaction. We show that gCayley graphs of a polygroup by two different generators are quasi-isometric. Finally, we express a connection between finitely generated polygroups and geodesic metric spaces.</p></abstract>

In this paper, we introduce a geodesic metric space called generalized Cayley graph (gCay(P,S)) on a finitely generated polygroup. We define a hyperaction of polygroup on gCayley graph and give some properties of this hyperaction. We show that gCayley graphs of a polygroup by two different generators are quasi-isometric. Finally, we express a connection between finitely generated polygroups and geodesic metric spaces.

On geometric polygroups

University of Defence in Brno Kounicova 65

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"On geometric polygroups"}

In this paper, we introduce a geodesic metric space called generalized Cayley graph (gCay(P,S)) on a finitely generated polygroup. We define a hyperaction of...

On geometric polygroups

Published Online: Apr 09, 2020

Page range: 17 - 33

Received: May 04, 2019

Accepted: Jul 23, 2019

DOI: https://doi.org/10.2478/auom-2020-0002

Keywords
polygroup, gCayley graph, hyperaction, geodesic metric space, quasi-isometry

© 2020 F. Arabpur et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On geometric polygroups

Published Online: Apr 09, 2020

Page range: 17 - 33

Received: May 04, 2019

Accepted: Jul 23, 2019

DOI: https://doi.org/10.2478/auom-2020-0002

Keywordspolygroup, gCayley graph, hyperaction, geodesic metric space, quasi-isometry

© 2020 F. Arabpur et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
polygroup, gCayley graph, hyperaction, geodesic metric space, quasi-isometry