Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/wiley/unsolvable-problems-about-small-cancellation-and-word-hyperbolic-jEa7HZk0HE
References (14)
-
S. Gersten, H. Short (1990)
Small cancellation theory and automatic groupsInventiones mathematicae, 102
-
Charles Miller (1992)
Decision Problems for Groups — Survey and Reflections -
Charles Miller (1971)
On Group-Theoretic Decision Problems and Their Classification. -
F. Grunewald (1978)
On Some Groups which cannot be Finitely PresentedJournal of The London Mathematical Society-second Series
-
G. Baumslag, W. Boone, B. Neumann (1959)
Some Unsolvable Problems about Elements and Subgroups of Groups.Mathematica Scandinavica, 7
-
B. Neumann (1958)
Review: Michael O. Rabin, Recursive Unsolvability of Group Theoretic ProblemsJournal of Symbolic Logic, 23
-
G. Baumslag, S. Gersten, Michael Shapiro, H. Short (1991)
Automatic groups and amalgamsJournal of Pure and Applied Algebra, 76
-
R. Bieri (1981)
Homological dimension of discrete groups -
J. Britton (1969)
Review: Gilbert Baumslag, W. W. Boone, B. H. Neumann, Some Unsolvable Problems about Elements and Subgroups of GroupsJournal of Symbolic Logic, 34
-
G. Baumslag, J. Roseblade (1984)
Subgroups of Direct Products of Free GroupsJournal of The London Mathematical Society-second Series
-
(1987)
Hyperbolic groups', Essays on group theory -
(1992)
Word processing in groups (Jones and Bartlett -
E. Rips (1982)
Subgroups of small Cancellation GroupsBulletin of The London Mathematical Society, 14
-
M. Rabin (1958)
Recursive Unsolvability of Group Theoretic ProblemsAnnals of Mathematics, 67
- Publisher
- Wiley
- Copyright
- © London Mathematical Society
- ISSN
- 0024-6093
- eISSN
- 1469-2120
- DOI
- 10.1112/blms/26.1.97
- Publisher site
- See Article on Publisher Site
Abstract
We apply a construction of Rips to show that a number of algorithmic problems concerning certain small cancellation groups and, in particular, word hyperbolic groups, are recursively unsolvable. Given any integer k > 2, there is no algorithm to determine whether or not any small cancellation group can be generated by either two elements or more than k elements. There is a small cancellation group E such that there is no algorithm to determine whether or not any finitely generated subgroup of E is all of E, or is finitely presented, or has a finitely generated second integral homology group.
Journal
Bulletin of the London Mathematical Society – Wiley
Published: Jan 1, 1994