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Primitive groups, graph endomorphisms and synchronization (2016)
Journal Article
Aroújo, J., Bentz, W., Cameron, P. J., Royle, G., & Schaefer, A. (2016). Primitive groups, graph endomorphisms and synchronization. Proceedings of the London Mathematical Society, 113(6), 829-867. https://doi.org/10.1112/plms/pdw040

© 2016 London Mathematical Society. Let Ω be a set of cardinality n, G be a permutation group on Ω and f : Ω → Ω be a map that is not a permutation. We say that G synchronizes f if the transformation semigroup 〈G, f〉 contains a constant map, and th... Read More about Primitive groups, graph endomorphisms and synchronization.

Directed graphs of inner translations of semigroups (2016)
Journal Article
Araújo, J., Bentz, W., & Konieczny, J. (2017). Directed graphs of inner translations of semigroups. Semigroup Forum, 94(3), 650-673. https://doi.org/10.1007/s00233-016-9821-x

A mapping α: S → S is called a Cayley function if there exist an associative operation µ: S x S → S and an element a ϵ S such that α(x) = µ(a, x) for every x ϵ S. The aim of the paper is to give a characterization of Cayley functions in terms of thei... Read More about Directed graphs of inner translations of semigroups.