11.15 (1990)

It is known that for each prime number $p$ there exists a series $a_1, a_2, \dots$ of words in two variables such that the finite group $G$ has abelian Sylow $p$-subgroups if and only if $a_k(G) = 1$ for almost all $k$. For $p = 2$ such a series is known explicitly (R. Brandl, J. Austral. Math. Soc., 31 (1981), 464–469). What about $p > 2$?