Browse > Article
http://dx.doi.org/10.11568/kjm.2021.29.3.577

RIGHT-ANGLED ARTIN GROUPS ON PATH GRAPHS, CYCLE GRAPHS AND COMPLETE BIPARTITE GRAPHS  

Lee, Eon-Kyung (Department of Mathematics Sejong University)
Lee, Sang-Jin (Department of Mathematics Konkuk University)
Publication Information
Korean Journal of Mathematics / v.29, no.3, 2021 , pp. 577-580 More about this Journal
Abstract
For a finite simplicial graph 𝚪, let G(𝚪) denote the right-angled Artin group on the complement graph of 𝚪. For path graphs Pk, cycle graphs Cℓ and complete bipartite graphs Kn,m, this article characterizes the embeddability of G(Kn,m) in G(Pk) and in G(Cℓ).
Keywords
right-angled Artin groups; embeddability; extension graphs;
Citations & Related Records
연도 인용수 순위
  • Reference
1 M. Casals-Ruiz, A. Duncan and I. Kazachkov, Embeddings between partially commutative groups: two counterexamples, J. Algebra. 390 (2013), 87-99.   DOI
2 R. Charney and K. Vogtmann, Finiteness properties of automorphism groups of rightangled Artin groups, Bull. Lond. Math. Soc. 41 (2009), 94-102.   DOI
3 J. Crisp, M. Sageev and M. Sapir, Surface subgroups of right-angled Artin groups, Internat. J. Algebra Comput. 18 (2008), 443-491.   DOI
4 C. Droms, Isomorphisms of graph groups, Proc. Amer. Math. Soc. 100 (1987), 407-408.   DOI
5 T. Katayama, Right-angled Artin groups and full subgraphs of graphs, J. Knot Theory Ramifications. 26 (2017), 1750059.   DOI
6 T. Katayama, Embeddability of right-angled Artin groups on the complements of linear forests, J. Knot Theory Ramifications. 27 (2018), 1850010.   DOI
7 S.-h. Kim, Co-contractions of graphs and right-angled Artin groups, Algebr. Geom. Topol. 8 (2008), 849--868.   DOI
8 S.-h. Kim and T. Koberda, Embedability between right-angled Artin groups, Geom. Topol. 17 (2013), 493-530.   DOI
9 S.-h. Kim and T. Koberda, Anti-trees and right-angled Artin subgroups of braid group, Geom. Topol. 19 (2015), 3289-3306.   DOI
10 E.-K. Lee and S.-J. Lee, Path lifting properties and embedding between RAAGs, J. Algebra. 448 (2016), 575-594.   DOI
11 E.-K. Lee and S.-J. Lee, Embeddability of right-angled Artin groups on complements of trees, Internat. J. Algebra Comput. 28 (2018), 381-394.   DOI
12 H. Servatius, Automorphisms of graph groups, J. Algebra. 126 (1989), 179-197.   DOI