Abstract
The Reidemeister orbit set plays a crucial role in the Nielsen type theory of periodic orbits, much as the Reidemeister set does in Nielsen fixed point theory. Let f : G $\longrightarrow$ G be an endomorphism between the fundamental group of the mapping torus. Extending Jiang and Ferrario's works on Reidemeister sets, we obtain algebraic results such as addition formulae for Reidemeister orbit sets of f relative to Reidemeister sets on suspension groups. In particular, if f is an automorphism, an similar formula for Reidemeister orbit sets of f relative to Reidemeister sets on given groups is also proved.
