Synchronization 2: Permutation groups
نویسنده
چکیده
Notation Ω will denote a set (often the set The image of an element v ∈ Ω under a permutation g of Ω will be denoted by vg. So if g and h are permutations, and we define composition by the rule that gh means " apply g, then h " , then v(gh) = (vg)h.
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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 summ...
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