Standard Words and Abelian Powers in Sturmian Words

We give three descriptions of the factors of a Sturmian word that are standard words. We also show that all Sturmian words are so-called everywhere abelian krepetitive for all integers k ≥ 1, that is, all sufficiently long factors have an abelian kth power as a prefix. More precisely, given a Sturmian word t and an integer k, there exist two integers `1 and `2 such that each position in t has an abelian kth power with abelian period `1 or `2.