Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Small cancellation groups and
translation numbers


Author: Ilya Kapovich
Journal: Trans. Amer. Math. Soc. 349 (1997), 1851-1875
MSC (1991): Primary 20F06; Secondary 20F10, 20F32
MathSciNet review: 1357396
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we prove that C(4)-T(4)-P, C(3)-T(6)-P and C(6)-P small cancellation groups are translation discrete in the strongest possible sense and that in these groups for any $g$ and any $n$ there is an algorithm deciding whether or not the equation $x^{n}=g$ has a solution. There is also an algorithm for calculating for each $g$ the maximum $n$ such that $g$ is an $n$-th power of some element. We also note that these groups cannot contain isomorphic copies of the group of $p$-adic fractions and so in particular of the group of rational numbers. Besides we show that for $C^{\prime \prime }(4)-T(4)$ and $C''(3)-T(6)$ groups all translation numbers are rational and have bounded denominators.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 20F06, 20F10, 20F32

Retrieve articles in all journals with MSC (1991): 20F06, 20F10, 20F32


Additional Information

Ilya Kapovich
Affiliation: Department of Mathematics, Graduate School and University Center of the City University of New York, 33 West 42nd Street, New York, New York 10036
Address at time of publication: Department of Mathematics, Hill Center, Busch Campus, Rutgers University at New Brunswick, Piscataway, New Jersey 08854
Email: ilya@groups.sci.ccny.cuny.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-97-01653-X
PII: S 0002-9947(97)01653-X
Received by editor(s): May 26, 1994
Received by editor(s) in revised form: October 30, 1995
Additional Notes: This research was supported by the Robert E. Gilleece Fellowship at the CUNY Graduate Center.
Article copyright: © Copyright 1997 American Mathematical Society