Résumé
We study the avoidability of long$k$ -abelian-squares and$k$ -abelian-cubes on binary and ternary alphabets. For$k=1$ , these are Mäkelä's questions. We show that one cannot avoid abelian-cubes of abelian period at least$2$in infinite binary words, and therefore answering negatively one question from Mäkelä. Then we show that one can avoid$3$ -abelian-squares of period at least$3$in infinite binary words and$2$ -abelian-squares of period at least 2 in infinite ternary words. Finally we study the minimum number of distinct$k$ -abelian-squares that must appear in an infinite binary word.