Small cancellation groups and translation numbers
Author:
Ilya Kapovich
Journal:
Trans. Amer. Math. Soc. 349 (1997), 18511875
MSC (1991):
Primary 20F06; Secondary 20F10, 20F32
MathSciNet review:
1357396
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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 and any there is an algorithm deciding whether or not the equation has a solution. There is also an algorithm for calculating for each the maximum such that is an th power of some element. We also note that these groups cannot contain isomorphic copies of the group of adic fractions and so in particular of the group of rational numbers. Besides we show that for and groups all translation numbers are rational and have bounded denominators.
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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/S000299479701653X
PII:
S 00029947(97)01653X
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
