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title
SymOmega
description
just another maths blog
image
site name
SymOmega
author
updated
2026-02-21 04:35:35
raw text
SymOmega – just another maths blog Skip to content SymOmega just another maths blog Spreading groups This is a follow-up to the work some of us at UWA have been doing on subproblems to do with the “synchronising hierarchy” of permutation groups. In an earlier post , we announced the discovery of synchronising groups of diagonal type. The definitions of synchronising/separating/spreading came about from the study of synchronising words for finite-state automata. Motivated by the Černý Conjecture on the length of reset words in synchronising automata, Arnold and Steinberg, and independently Araújo, introduced the notion of a synchronising group. We say that a permutation group is synchronising if for any non-bijective transformation , the transformation semigroup is synchronising; that is, it contains a constant map (aka. reset word). It was observed in Peter Neumann’s seminal article in 2009 that a synchronising permutation group is primitive. Moreover, the pos...
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