A user's guide to cloning systems

Abstract

In joint work of the author with Stefan Witzel, a procedure was developed for building new examples of groups in the extended family of R. Thompson's groups, using what we termed \emph{cloning systems}. These new Thompson-like groups can be thought of as limits of families of groups, though unlike other limiting processes, e.g., direct limits, these tend to be well behaved with respect to finiteness properties. In this expository note, we distill the crucial parts of that 50-page paper into a more digestible form, for those curious to understand the construction but less curious about the gritty details. We also give one new example, of a cloning system involving signed symmetric groups.