Divergent coindex sequence for dynamical systems

When a finite group freely acts on topological space, we can define its index and coindex. They roughly measure the size of given action. We explore interaction between this theory dynamics. Given fixed-point free dynamical system, set [Formula: see text]-periodic points admits natural action text] for each prime number text]. are interested in growth coindex as Our main result shows that there exists system having divergent sequence. This solves problem posed by M. Tsukamoto, Tsutaya Yoshinaga, text]-index, dynamics marker property, preprint (2020), arXiv: 2012.15372.