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Wreath products and the non-coprime k(GV) problem
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics , First View
- Published online by Cambridge University Press:
- 26 November 2025, pp. 1-17
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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 Xn. 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.
