On the number of conjugacy classes of a primitive permutation group

Garzoni, Daniele; Gill, Nick

doi:10.1017/prm.2021.74

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Probabilistic Methods1

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2023

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Cited by 2 publications

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“…In this case, [29, Theorem 1.2] implies that , except when or . In the latter two cases, it is easy to check (26).…”

Section: Probabilistic Methodsmentioning

confidence: 96%

Base sizes of primitive groups of diagonal type

Huang

2023

Forum of Mathematics, Sigma

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Let G be a permutation group on a finite set $\Omega $ . The base size of G is the minimal size of a subset of $\Omega $ with trivial pointwise stabiliser in G. In this paper, we extend earlier work of Fawcett by determining the precise base size of every finite primitive permutation group of diagonal type. In particular, this is the first family of primitive groups arising in the O’Nan–Scott theorem for which the exact base size has been computed in all cases. Our methods also allow us to determine all the primitive groups of diagonal type with a unique regular suborbit.

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“…In this case, [29, Theorem 1.2] implies that , except when or . In the latter two cases, it is easy to check (26).…”

Section: Probabilistic Methodsmentioning

confidence: 96%