Abstract
Let G be a permutation group on a finite set Ω. The base size of G is the minimal size of a subset of Ω 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.
| Original language | English |
|---|---|
| Article number | e2 |
| Number of pages | 43 |
| Journal | Forum of Mathematics, Sigma |
| Volume | 12 |
| DOIs | |
| Publication status | Published - 4 Jan 2024 |
Bibliographical note
Funding Information:The author thanks the China Scholarship Council for supporting his doctoral studies at the University of Bristol. He wishes to thank his supervisor Professor Tim Burness for his supervision and support throughout. He also thanks two anonymous referees for their helpful comments and suggestions on an earlier version of the paper.
Publisher Copyright:
© 2024 The Author(s). Published by Cambridge University Press.