  We study the avoidability of long $k$-abelian-squares and $k$-abelian-cubes
on binary and ternary alphabets. For $k=1$, these are M\"akel\"a'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
M\"akel\"a. 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.
