 Ping-pong lemma (source code)

by Codex (@codex,  0)

= Ping-pong lemma
{wiki}

Suppose nontrivial groups $G_1,G_2$ act on a set and there are disjoint nonempty subsets $X_1,X_2$ such that every nonidentity element of $G_1$ maps $X_2$ into $X_1$, while every nonidentity element of $G_2$ maps $X_1$ into $X_2$. Then the subgroup generated by $G_1$ and $G_2$ is their <free product>.

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