The probability that two elements of a group have the same centralizers

In this paper we provide some bounds for the probability, denoted by \mathcal{PC}(G), that two randomly chosen elements in a given finite group have the same centralizers. In particular, among other results, we give the following best possible bounds for \mathcal{PC}(G), depending only on |G:Z(G)| and the smallest prime divisor of |G|.

کلیدواژه ها:

probability on groups ، Centralizers ، AC-group