Math 2.0

Proof

Proof of the Ping-pong lemma for infinite cyclic subgroups

Proof

This statement follows as a corollary of the version for general subgroups if we let Xi=Xi+∪Xi−X_{i} = X_{i}^{+} \cup X_{i}^{-} and let Hi=⟨ai⟩H_{i} = \langle a_{i}\rangle.

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Further reading

  1. Wikipedia, page 18786361, revision 1361203357, Ping-pong lemma, section Formal statements > The Ping-pong lemma for infinite cyclic subgroups > Proof. adopted
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ProvesThe Ping-pong lemma for infinite cyclic subgroups
Changed4 November 2026

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