Maximal abelian square-free words of short length

A word is called abelian square-free if it contains no two adjacent subwords which are permutations of each other. An abelian square-free word over an alphabet Σk which cannot be extended to the left or right with letters from Σk while remaining abelian square-free is called a maximal abelian square-free word. We prove, by an explicit construction, that the shortest maximal abelian square-free word over an alphabet of k letters has length at most 6k−10.