Groups with infinitely many types of fixed subgroups.
\textit{J. A. Shor} proved in his PhD thesis [On fixed subgroups of automorphisms in hyperbolic groups, Columbia Univ. (1999)] that given any hyperbolic group, then, there are only finitely many isomorphism types of subgroups that appear as fixed subgroups of automorphisms of this group. In the paper under review, the authors show that Shor's hypothesis on the group being hyperbolic cannot be weakened to the group being CAT(0) nor biautomatic. More precisely, they prove that there exists a group \(G\) acting freely and cocompactly on the Cartesian product of two trees such that infinitely many non-isomorphic groups appear as fixed subgroups of automorphisms of \(G\). (Such a group \(G\) is known to be CAT(0) and biautomatic.)
scientific article; zbMATH DE number 2147123