A note on the weak tracial Rokhlin property for finite group actions on simple unital C*-algebras

In this paper, we show that one of the conditions in the definition of weak tracial Rokhlin property for finite group actions on simple unital C*-algebras can be replaced by a seemingly weaker condition, or a seemingly stronger condition. As a corollary, this condition is redundant whenever the C*-algebra is not purely infinite. We also give a sufficient condition for the weak tracial Rokhlin property for finite group actions on simple unital C*-algebras to imply the tracial Rokhlin property.