In an HNN extension, every word containing a stable letter and having no pinch t−1ct or tdt−1 is nonidentity. In particular, the natural map from the base group to its HNN extension is injective.
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- HNN extension
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- Adjoining a root by an HNN extension
- Centralizing HNN extension detects subgroup membership
- Countable torsion-free embedding with two conjugacy classes
- Cyclically reduced sequence in an HNN extension
- Finite presentation of a centralizing HNN extension detects finite generation of its associated subgroup
- Higman group as an amalgam of iterated HNN extensions
- Intersection and join of benign subgroups
- Iterated endomorphism kernels in BS(2,3)
- Non-Hopfian group
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- Permutation proof of HNN normal form uniqueness
- Pinch in an HNN extension
- Recursive simple envelope by cyclic HNN extensions
- Reduced sequence in an HNN extension
- Torsion in an HNN extension
- Two-generator HNN embedding
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