Synchronising primitive groups of diagonal type exist

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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 languageEnglish
Pages (from-to)1131-1144
Number of pages14
JournalBulletin of the London Mathematical Society
Issue number3
Publication statusPublished - Jun 2022


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