Simple groups of dynamical origin Academic Article uri icon

abstract

  • We associate with every tale groupoid $mathfrak{G}$ two normal subgroups $mathsf{S}(mathfrak{G})$ and $mathsf{A}(mathfrak{G})$ of the topological full group of $mathfrak{G}$, which are analogs of the symmetric and alternating groups. We prove that if $mathfrak{G}$ is a minimal groupoid of germs (e.g., of a group action), then $mathsf{A}(mathfrak{G})$ is simple and is contained in every non-trivial normal subgroup of the full group. We show that if $mathfrak{G}$ is expansive (e.g., is the groupoid of germs of an expansive action of a group), then $mathsf{A}(mathfrak{G})$ is finitely generated. We also show that $mathsf{S}(mathfrak{G})/mathsf{A}(mathfrak{G})$ is a quotient of $H_{0}(mathfrak{G},mathbb{Z}/2mathbb{Z})$.

published proceedings

  • ERGODIC THEORY AND DYNAMICAL SYSTEMS

author list (cited authors)

  • Nekrashevych, V.

citation count

  • 18

complete list of authors

  • Nekrashevych, V

publication date

  • March 2019