Simple groups of dynamical origin
Group Theory
2017-02-08 v2 Dynamical Systems
Abstract
We associate with every etale groupoid G two normal subgroups S(G) and A(G) of the topological full group of G, which are analogs of the symmetric and alternating groups. We prove that if G is a minimal groupoid of germs (e.g., of a group action), then A(G) is simple and is contained in every non-trivial normal subgroup of the full group. We show that if G is expansive (e.g., is the groupoid of germs of an expansive action of a group), then A(G) is finitely generated. We also show that S(G)/A(G) is a quotient of H_0(G, Z/2Z).
Cite
@article{arxiv.1511.08241,
title = {Simple groups of dynamical origin},
author = {Volodymyr Nekrashevych},
journal= {arXiv preprint arXiv:1511.08241},
year = {2017}
}
Comments
25 pages, 3 figures