2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67835For any $C\in[0,\infty]$ a compact group automorphism $T:X\to X$ is constructed with the property that $$ \frac{1}{n}\log|\{x\in X\mid T^n(x)=x\}|\longrightarrow C. $$ This may be interpreted as a combinatorial analogue of the (still open) problem of whether compact group automorphisms exist with any given topological entropy.amsart latex 6 pagesDynamical SystemsNumber Theory37C35; 22D40; 11N13text