Synchronising primitive groups of diagonal type exist

John Bamberg; Michael Giudici; Jesse Lansdown; Gordon F. Royle

doi:10.1112/blms.12619

Synchronising primitive groups of diagonal type exist

John Bamberg, Michael Giudici, Jesse Lansdown, Gordon F. Royle

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

Every synchronising permutation group is primitive and of one of three types: affine, almost simple, or diagonal. We exhibit the first known example of a synchronising diagonal type group. More precisely, we show that (Formula presented.) acting in its diagonal action on (Formula presented.) is separating, and hence synchronising, for (Formula presented.) and (Formula presented.). Furthermore, we show that such groups are non-spreading for all prime powers (Formula presented.).

Original language	English
Pages (from-to)	1131-1144
Number of pages	14
Journal	Bulletin of the London Mathematical Society
Volume	54
Issue number	3
DOIs	https://doi.org/10.1112/blms.12619
Publication status	Published - Jun 2022

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10.1112/blms.12619

https://arxiv.org/abs/2104.13355

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abstract = "Every synchronising permutation group is primitive and of one of three types: affine, almost simple, or diagonal. We exhibit the first known example of a synchronising diagonal type group. More precisely, we show that (Formula presented.) acting in its diagonal action on (Formula presented.) is separating, and hence synchronising, for (Formula presented.) and (Formula presented.). Furthermore, we show that such groups are non-spreading for all prime powers (Formula presented.).",

author = "John Bamberg and Michael Giudici and Jesse Lansdown and Royle, {Gordon F.}",

note = "Funding Information: This work forms part of an Australian Research Council Discovery Project DP200101951. Publisher Copyright: {\textcopyright} 2022 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.",

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Y1 - 2022/6

N2 - Every synchronising permutation group is primitive and of one of three types: affine, almost simple, or diagonal. We exhibit the first known example of a synchronising diagonal type group. More precisely, we show that (Formula presented.) acting in its diagonal action on (Formula presented.) is separating, and hence synchronising, for (Formula presented.) and (Formula presented.). Furthermore, we show that such groups are non-spreading for all prime powers (Formula presented.).

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Synchronising primitive groups of diagonal type exist

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The synchronisation hierarchy of permutation groups

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Synchronising primitive groups of diagonal type exist

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The synchronisation hierarchy of permutation groups

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