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PreprintCC BY-NC-ND 4.0arXiv

A simple acylindrical recipe for non-split characteristic $2$ sharply k-transitive actions and their generalizations

  • J de la Nuez Gonzalez
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Abstract

We provide a fairly simple list of conditions on a group G acting acylindrically on a δ-hyperbolic metric space sufficient for the group to admit an action on a set that is k-sharp, transitive on k-sets and has the property that for any k-set A the setwise stabilizer of A acts on A as prescribed by some fixed subgroup of the group of permutations of k elements. In particular, this yields a large class of non-split sharply $2$ and $3$-transitive actions containing many finitely presented groups, and allows us to characterize sharp $2$-transitivity within the class of hyperbolic groups that do not contain a copy of C2× C2.

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Cite

BibTeXRIS
BibTeX
@misc{gonzalez2026simple,
  title = {{A simple acylindrical recipe for non-split characteristic $2$ sharply $k$-transitive actions and their generalizations}},
  author = {J de la Nuez Gonzalez},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.10114},
  eprint = {2608.10114},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.10114},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - A simple acylindrical recipe for non-split characteristic $2$ sharply k-transitive actions and their generalizations
AU  - J de la Nuez Gonzalez
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2608.10114
UR  - https://arxiv.org/abs/2608.10114
AB  - We provide a fairly simple list of conditions on a group G acting acylindrically on a δ-hyperbolic metric space sufficient for the group to admit an action on a set that is k-sharp, transitive on k-sets and has the property that for any k-set A the setwise stabilizer of A acts on A as prescribed by some fixed subgroup of the group of permutations of k elements. In particular, this yields a large class of non-split sharply $2$ and $3$-transitive actions containing many finitely presented groups, and allows us to characterize sharp $2$-transitivity within the class of hyperbolic groups that do not contain a copy of C_2× C_2.
ER  -