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Let $X$ be a finite CW complex, $n \ge 2$, and $\Sigma_n$ be the permutation group on $n$ symbols. Let $X^{(n)}=X^n/\Sigma_n$ be the quotient of the natural action of $\Sigma_n$ on $X^n$. We call $X^{(...

Let $\pi\subseteq\Sigma_r$ and $V$ be a right $\pi$-space. We may assume that $V$ is free, if necessary. Consider the morphism of singular chain complexes (over a fixed commutative ring) $$f:C_*(V) \...