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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



$ {\bf R}$-trees, small cancellation, and convergence

Author: Andrew Chermak
Journal: Trans. Amer. Math. Soc. 347 (1995), 4515-4531
MSC: Primary 20F10; Secondary 20E08, 57M07
MathSciNet review: 1316846
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Abstract: The "metric small cancellation hypotheses" of combinatorial group theory imply, when satisfied, that a given presentation has a solvable Word Problem via Dehn's Algorithm. The present work both unifies and generalizes the small cancellation hypotheses, and analyzes them by means of group actions on trees, leading to the strengthening of some classical results.

References [Enhancements On Off] (What's this?)

  • [1] R. Alperin and H. Bass, Length functions of group actions on $ \Lambda $-trees, Combinatorial Group Theory and Topology (Alta, Utah, 1984), Ann. of Math. Studies, no. 111, Princeton Univ. Press, Princeton, NJ, 1987, pp. 265-378. MR 895622 (89c:20057)
  • [2] Andrew Chermak, Triangles of groups, preprint. MR 1316847 (96g:20048)
  • [3] -, Colimits of sporadic triangles of groups, preprint.
  • [4] R. C. Lyndon and P. E. Schupp, Combinatorial group theory, Springer-Verlag, Berlin and New York, 1977. MR 0577064 (58:28182)

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