Korean Journal of Mathematics

  • 제29권3호
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  • Pages.577-580
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  • 2021
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  • 1976-8605(pISSN)
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  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
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RIGHT-ANGLED ARTIN GROUPS ON PATH GRAPHS, CYCLE GRAPHS AND COMPLETE BIPARTITE GRAPHS

  • 투고 : 2021.08.04
  • 심사 : 2021.08.30
  • 발행 : 2021.09.30
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⟨ 이전 논문 다음 논문 ⟩

초록

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).

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과제정보

This work was partially supported by NRF-2018R1D1A1B07043291. This work was partially supported by NRF-2018R1D1A1B07043268.

참고문헌

  1. M. Casals-Ruiz, A. Duncan and I. Kazachkov, Embeddings between partially commutative groups: two counterexamples, J. Algebra. 390 (2013), 87-99. https://doi.org/10.1016/j.jalgebra.2013.04.036
  2. R. Charney and K. Vogtmann, Finiteness properties of automorphism groups of rightangled Artin groups, Bull. Lond. Math. Soc. 41 (2009), 94-102. https://doi.org/10.1112/blms/bdn108
  3. J. Crisp, M. Sageev and M. Sapir, Surface subgroups of right-angled Artin groups, Internat. J. Algebra Comput. 18 (2008), 443-491. https://doi.org/10.1142/S0218196708004536
  4. C. Droms, Isomorphisms of graph groups, Proc. Amer. Math. Soc. 100 (1987), 407-408. https://doi.org/10.1090/S0002-9939-1987-0891135-1
  5. T. Katayama, Right-angled Artin groups and full subgraphs of graphs, J. Knot Theory Ramifications. 26 (2017), 1750059. https://doi.org/10.1142/S0218216517500596
  6. T. Katayama, Embeddability of right-angled Artin groups on the complements of linear forests, J. Knot Theory Ramifications. 27 (2018), 1850010. https://doi.org/10.1142/S0218216518500104
  7. S.-h. Kim, Co-contractions of graphs and right-angled Artin groups, Algebr. Geom. Topol. 8 (2008), 849--868. https://doi.org/10.2140/agt.2008.8.849
  8. S.-h. Kim and T. Koberda, Embedability between right-angled Artin groups, Geom. Topol. 17 (2013), 493-530. https://doi.org/10.2140/gt.2013.17.493
  9. S.-h. Kim and T. Koberda, Anti-trees and right-angled Artin subgroups of braid group, Geom. Topol. 19 (2015), 3289-3306. https://doi.org/10.2140/gt.2015.19.3289
  10. E.-K. Lee and S.-J. Lee, Path lifting properties and embedding between RAAGs, J. Algebra. 448 (2016), 575-594. https://doi.org/10.1016/j.jalgebra.2015.09.010
  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. https://doi.org/10.1142/S0218196718500182
  12. H. Servatius, Automorphisms of graph groups, J. Algebra. 126 (1989), 179-197. https://doi.org/10.1016/0021-8693(89)90319-0