Comeagre conjugacy classes and free products with amalgamation

Dugald MacPherson, Simon Thomas

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


The main theorem is that if G is a Polish group with a comeagre conjugacy class, and G acts without inversions on some tree T, then for every g∈G there is a vertex of T fixed by g. In particular, such a group cannot be written non-trivially as a free product with amalgamation. The same conclusion holds if G is the automorphism group of an ω-categorical structure and some open subgroup of G has a comeagre conjugacy class.

Original languageEnglish (US)
Pages (from-to)135-142
Number of pages8
JournalDiscrete Mathematics
Issue number1-3
StatePublished - Mar 6 2005

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


  • Action on tree
  • Free product with amalgamation
  • Polish group
  • ω-Categorical

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