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In this work, we prove that every SFT, sofic shift, and strongly irreducibleshift on locally finite groups has strong dynamical properties. Theseproperties include that every sofic shift is an SFT, every SFT is stronglyirreducible, every strongly irreducible shift is an SFT, every SFT is entropyminimal, and every SFT has a unique measure of maximal entropy, among others.In addition, we show that if every SFT on a group is strongly irreducible, orif every sofic shift is an SFT, then the group must be locally finite, and thisextends to all of the properties we explore. These results are collected in twomain theorems which characterizes the local finiteness of groups by purelydynamical properties. In pursuit of these results, we present a formalconstruction of \textit{free extension} shifts on a group $G$, which takes ashift on a subgroup $H$ of $G$, and naturally extends it to a shift on all of$G$.

Shifts of Finite Type on Locally Finite Groups