Permutation groups and transformation semigroups
نویسنده
چکیده
In collaboration with João Araújo and others, I have been thinking about relations between permutation groups and transformation semigroups. In particular, what properties of a permutation group G on a set Ω guarantee that, if f is any non-permutation on Ω (or perhaps any non-permutation of rank k), then the transformation semigroup 〈G, f〉 has specified properties. There is far too much to summarise in a short talk, but I will try to say a little about two topics: Synchronization: for example, what are the non-syncnronizing ranks of a permutation group, the ranks k for which 〈G, f〉 is nonsynchronizing for some element f of rank k? Regularity: for example, which permutation groups G have the property that, for any element f of rank k, f has a quasi-inverse in 〈G, f〉?
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