On Whitehead’s cut vertex lemma
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Rylee Alanza Lyman
Abstract
One version of Whitehead’s famous cut vertex lemma says that if an element of a free group is part of a free basis, then a certain graph associated to its conjugacy class that we call the star graph is either disconnected or has a cut vertex. We state and prove a version of this lemma for conjugacy classes of elements and convex-cocompact subgroups of groups acting cocompactly on trees with finitely generated edge stabilizers.
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Communicated by: Dessislava Kochloukova
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© 2023 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Curvature distribution and hyperbolicity
- On Whitehead’s cut vertex lemma
- Abelian splittings and JSJ-decompositions of finitely presented Bestvina–Brady groups
- On endomorphisms of the direct product of two free groups
-
The
- A note on torsion length and torsion subgroups
- On the separability of subgroups of nilpotent groups by root classes of groups
- The Addition Theorem for two-step nilpotent torsion groups
- A bound for the orders of centralizers of irreducible subgroups of algebraic groups
- The average character degree of finite groups and Gluck’s conjecture
- Character degrees of normally monomial 𝑝-groups of maximal class
- Finite groups with an affine map of large order
- Classification of non-solvable groups whose power graph is a cograph
Articles in the same Issue
- Frontmatter
- Curvature distribution and hyperbolicity
- On Whitehead’s cut vertex lemma
- Abelian splittings and JSJ-decompositions of finitely presented Bestvina–Brady groups
- On endomorphisms of the direct product of two free groups
-
The
- A note on torsion length and torsion subgroups
- On the separability of subgroups of nilpotent groups by root classes of groups
- The Addition Theorem for two-step nilpotent torsion groups
- A bound for the orders of centralizers of irreducible subgroups of algebraic groups
- The average character degree of finite groups and Gluck’s conjecture
- Character degrees of normally monomial 𝑝-groups of maximal class
- Finite groups with an affine map of large order
- Classification of non-solvable groups whose power graph is a cograph
