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Beauville Structures for Quotients of Generalised GGS-groups

Di Domenico, Elena ; Gül, Şükran and Thillaisundaram, Anitha LU (2024) In Advances in Group Theory and Applications 18. p.3-40
Abstract

A finite group with a Beauville structure gives rise to a certain compact complex surface called a Beauville surface. Gül and Uria-Albizuri showed that quotients of the periodic Grigorchuk–Gupta–Sidki (GGS-)groups that act on the p-adic tree, for p an odd prime, admit Beauville structures. We extend their result by showing that quotients of infinite periodic GGS-groups acting on pn-adic trees, for p any prime and n ≥ 2, also admit Beauville structures.

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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Beauville structure, finite p-group, groups acting on rooted trees
in
Advances in Group Theory and Applications
volume
18
pages
38 pages
publisher
Aracne Editrice
external identifiers
  • scopus:85195262425
ISSN
2499-1287
DOI
10.32037/agta-2024-001
language
English
LU publication?
yes
id
0b0e1f38-efe4-4191-ad92-ea6c8e152843
date added to LUP
2024-08-20 13:03:13
date last changed
2024-08-21 14:27:24
@article{0b0e1f38-efe4-4191-ad92-ea6c8e152843,
  abstract     = {{<p>A finite group with a Beauville structure gives rise to a certain compact complex surface called a Beauville surface. Gül and Uria-Albizuri showed that quotients of the periodic Grigorchuk–Gupta–Sidki (GGS-)groups that act on the p-adic tree, for p an odd prime, admit Beauville structures. We extend their result by showing that quotients of infinite periodic GGS-groups acting on p<sup>n</sup>-adic trees, for p any prime and n ≥ 2, also admit Beauville structures.</p>}},
  author       = {{Di Domenico, Elena and Gül, Şükran and Thillaisundaram, Anitha}},
  issn         = {{2499-1287}},
  keywords     = {{Beauville structure; finite p-group; groups acting on rooted trees}},
  language     = {{eng}},
  pages        = {{3--40}},
  publisher    = {{Aracne Editrice}},
  series       = {{Advances in Group Theory and Applications}},
  title        = {{Beauville Structures for Quotients of Generalised GGS-groups}},
  url          = {{http://dx.doi.org/10.32037/agta-2024-001}},
  doi          = {{10.32037/agta-2024-001}},
  volume       = {{18}},
  year         = {{2024}},
}