On the number of conjugacy classes of a primitive permutation group

Garzoni, Daniele and Gill, Nick (2022). On the number of conjugacy classes of a primitive permutation group. Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Early access).

DOI: https://doi.org/10.1017/prm.2021.74

Abstract

Let G be a primitive permutation group of degree n with nonabelian socle, and let k(G) be the number of conjugacy classes of G. We prove that either k(G)<n/2 and k(G)=o(n) as n→∞, or G belongs to explicit families of examples.

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