Geodesic
Base sizes of primitive groups of diagonal type
Forum of Mathematics, Sigma, Tome 12 (2024)

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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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     author = {Hong Yi Huang},
     title = {Base sizes of primitive groups of diagonal type},
     journal = {Forum of Mathematics, Sigma},
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     doi = {10.1017/fms.2023.121},
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     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2023.121/}
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Hong Yi Huang. Base sizes of primitive groups of diagonal type. Forum of Mathematics, Sigma, Tome 12 (2024). doi: 10.1017/fms.2023.121

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