Canadian Mathematical Bulletin· 2026Q2
Groups with fast-growing conjugator length functions
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- Q2SCImago
- 2026year
Short summary
Researchers constructed the first finitely presented groups with exponential conjugator length functions, specifically central extensions of F_m ⋊ F_2 groups.
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Key points
- First examples of finitely presented groups with exponential conjugator length functions are constructed.
- These groups are central extensions of F_m ⋊ F_2 (F_m semidirect product F_2).
- A fiber product construction generates a family of groups (Γ_k) with conjugator length functions growing according to the Grzegorczyk hierarchy.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract We construct the first examples of finitely presented groups whose conjugator length function is exponential; these are central extensions of groups of the form F m ⋊ F 2 $F_m\rtimes F_2$ upper F Subscript m Baseline right normal factor semidirect product upper F 2 . Further, we use a fiber product construction to exhibit a family of finitely presented groups Γ k $\Gamma _k$ normal upper Gamma Subscript k , where for each k , the conjugator length function of Γ k $\Gamma _k$ normal upper Gamma Subscript k grows like functions lying in the k -th level of the Grzegorczyk hierarchy of primitive recursive functions.
The authors' abstract, as published at the source. Canadian Mathematical Bulletin, 2026 · DOI ↗
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Field: Discrete Mathematics and Combinatorics
Discrete Mathematics and CombinatoricsMathematics