A space $X$ is called {it selectively pseudocompact} if for each sequence $(U_{n})_{nin mathbb{N}}$ of pairwise disjoint nonempty open subsets of $X$ there is a sequence $(x_{n})_{nin mathbb{N}}$ of points in $X$ such that $cl_X({x_n : n < omega}) setminus big(bigcup_{n < omega}U_n big) eq emptyset$ and $x_{n}in U_{n}$, for each $n < omega$. Countably compact space spaces are selectively pseudocompact and every selectively pseudocompact space is pseudocompact. We show, under the assumption of $CH$, that for every positive integer $k > 2$ there exists a topological group whose $k$-th power is countably compact but its $(k+1)$-st power is not selectively pseudocompact. This provides a positive answer to a question posed in cite{gt} in any model of $ZFC+CH$.
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