= Homotopy-group addition in a topological group
{title2=$[\alpha\beta]=[\alpha]+[\beta]$}
For $n\ge1$, pointwise multiplication of based cube maps into a <topological group> induces the ordinary addition in its <homotopy group> $\pi_n(G,e)$. Concatenation and pointwise multiplication share an identity and satisfy the interchange rule, so the <Eckmann-Hilton argument> identifies the two operations. In particular, the $m$-th power map induces multiplication by $m$ on every <homotopy group>, for all integers $m$.
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