Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-26T07:15:52.681Z Has data issue: false hasContentIssue false

ON THE RECOGNITION OF RIGHT-ANGLED ARTIN GROUPS

Published online by Cambridge University Press:  19 June 2019

MARTIN R. BRIDSON*
Affiliation:
Mathematical Institute, Andrew Wiles Building, Oxford OX2 6GG, Europe e-mail: [email protected]

Abstract

There does not exist an algorithm that can determine whether or not a group presented by commutators is a right-angled Artin group.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2019

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Baumslag, G. and Roseblade, J., Subgroups of direct products of free groups, J. London Math. Soc. 30(2) (1984), 4452.CrossRefGoogle Scholar
Boone, W. W., Certain simple unsolvable problems in group theory, I, II, III, IV, V, VI, Nederl. Akad.Wetensch Proc. 57 (1954), 231–237, 492–497; 58 (1955), 252–256, 571–577; 60 (1957), 22–27, 227232.Google Scholar
Borisov, V., Simple examples of groups with unsolvable word problem, Math. Zametki 6 (1969), 521532; English transl. Math. Notes 6 (1969), 768–775.Google Scholar
Day, M. and Wade, R., Subspace arrangements, BNS invariants, and pure symmetric outer automorphisms of right-angled Artin groups, Groups Geom. Dyn. 12 (2018), 173206.CrossRefGoogle Scholar
Kim, K. H. and Roush, F.W., Homology of certain algebras defined by graphs, J. Pure Appl. Algebra 17 (1980), 179186.CrossRefGoogle Scholar
Miller III, C. F., On group-theoretic decision problems and their classification, Annals of Mathematics Studies, vol. 68 (Princeton University Press, Princeton, NJ, 1971).Google Scholar
Miller III, C. F., Decision problems for groups: survey and reflections, in Algorithms and classification in combinatorial group theory (Baumslag, G. and Miller III, C. F., Editors), vol. 23 (MSRI Publications, Springer-Verlag, 1992), pp. 159.CrossRefGoogle Scholar
Mihailova, K. A., The occurrence problem for direct products of groups, Dokl. Akad. Nauk SSSR 119 (1958), 11031105.Google Scholar
Novikov, P. S., On the algorithmic unsolvability of the word problem in group theory, Trudy Mat. Inst. Steklov 44 (1955), 1143.Google Scholar