Constantinescu and Ilie (Bulletin EATCS 89, 167--170, 2006) introduced the
notion of an \emph{Abelian period} of a word. A word of length n over an
alphabet of size σ can have Θ(n2) distinct Abelian periods.
The Brute-Force algorithm computes all the Abelian periods of a word in time
O(n2×σ) using O(n×σ) space. We present an off-line
algorithm based on a \sel function having the same worst-case theoretical
complexity as the Brute-Force one, but outperforming it in practice. We then
present on-line algorithms that also enable to compute all the Abelian periods
of all the prefixes of w.Comment: Accepted for publication in Discrete Applied Mathematic