Work

Wreath products and the non-coprime k ( GV ) problem

Year: 2025

Type: article

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.

Source: Proceedings of the Royal Society of Edinburgh Section A Mathematics

DOI: 10.1017/prm.2025.10083

Authors: Nguyen N. Hung, Attila Maróti, Juan Martínez Madrid

Institutions: University of Akron, HUN-REN Alfréd Rényi Institute of Mathematics, Universitat de València

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550