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

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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 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:
https://doi.org/10.1090/S0002-9947-97-01653-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