Limit points in the range of the commuting probability function on finite groups
Abstract
If G is a finite group, then Pr(G) denotes the fraction of ordered pairs of elements of G which commute. We show that, if l ∈ (2/9,1] is a limit point of the function Pr on finite groups, then l ∈ and there exists an e = el > 0 such that Pr(G) ∈ (l - el, l) for any finite group G. These results lend support to some old conjectures of Keith Joseph.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.