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

Hung, Nguyen N. and Maróti, Attila and Martínez Madrid, Juan (2025) Wreath products and the non-coprime k ( GV ) problem. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS. ISSN 0308-2105 (In Press)

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Abstract

Let 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 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.

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