Topological groups with three relative commutativity degrees.

Suppose that G is a compact Hausdorff topological group and H is a closed subgroup of G. The relative commutativity degree of H in G, denoted by Pr(H;G), represents the probability that an element of H commutes with an element of G. Let D(G) be the set of all relative commutativity degrees of subgroups of G. In this paper, we will study the structure of topological groups that have exactly three relative commutativity degrees for their subgroups. In particular, we will show that for such groups, the centralizer of every non-central element is a maximal abelian subgroup. We will also provide examples of groups that have three relative commutativity degrees. [ABSTRACT FROM AUTHOR]