摘要

This paper is Appendix of the paper of T. Ceccherini-Silberstein, F. Scarabotti and F. Tolli [8]. We pay close attention on a special condition related to Gelfand pairs. Namely, we call a finite group G and its automorphism satisfy Condition () if the following condition is satisfied: if for , and are conjugate in G, then they are conjugate in . The main purpose of the note was to study the meanings of this condition, as well as showing many examples of G and which do (or do not) satisfy Condition (star).