Spreading primitive groups of diagonal type do not exist

John Bamberg, Saul D. Freedman, Michael Giudici

Research output: Contribution to journalArticlepeer-review


The synchronization hierarchy of finite permutation groups consists of classes of groups lying between -transitive groups and primitive groups. This includes the class of spreading groups, which are defined in terms of sets and multisets of permuted points, and which are known to be primitive of almost simple, affine or diagonal type. In this paper, we prove that in fact no spreading group of diagonal type exists. As part of our proof, we show that all non-abelian finite simple groups, other than six sporadic groups, have a transitive action in which a proper normal subgroup of a point stabilizer is supplemented by all corresponding two-point stabilizers.

Original languageEnglish
Number of pages11
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
Publication statusE-pub ahead of print - 26 Apr 2024


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