Small cancellation groups and translation numbers

Ilya Kapovich

Research output: Contribution to journalArticlepeer-review


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 xn = 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"'(4) - T(4) and C"(3) - T(6) groups all translation numbers are rational and have bounded denominators.

Original languageEnglish (US)
Pages (from-to)1851-1875
Number of pages25
JournalTransactions of the American Mathematical Society
Issue number5
StatePublished - 1997
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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