Wreath products and the non-coprime <i>k</i> ( <i>GV</i> ) problem
Abstract Let $G = X \wr H$ be the wreath product of a nontrivial finite group X with k conjugacy classes and a transitive permutation group H of degree n acting on the set of n direct factors of X n . If H is semiprimitive, then $k(G) \leq k^n$ for every sufficiently large n or k . This result solves a case of the non-coprime k ( GV ) problem and provides an affirmative answer to a question of Garzoni and Gill for semiprimitive permutation groups. The proof does not require the classification of finite simple groups.
Authors
- Hung Ngoc Nguyen (ORCID: https://orcid.org/0000-0002-5950-6271)
- Attila Maróti (ORCID: https://orcid.org/0000-0002-6896-3378)
- Juan José Prieto Martínez (ORCID: https://orcid.org/0000-0003-4954-1599)
Institutions
- University of Akron (US)
- HUN-REN Alfréd Rényi Institute of Mathematics (HU)
- Universitat de València (ES)
Publication Details
- Journal
- Proceedings of the Royal Society of Edinburgh Section A Mathematics
- Published
- 2025-11-26
- DOI
- https://doi.org/10.1017/prm.2025.10083
- Primary Topic
- Finite Group Theory Research
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Generalitat Valenciana
- Ministerio de Ciencia e Innovación
- Nemzeti Kutatási Fejlesztési és Innovációs Hivatal
- European Regional Development Fund
- Agencia Estatal de Investigación
- National Research, Development and Innovation Office