Square-Free Non-Cayley Numbers. On Vertex-Transitive Non-Cayley Graphs of Square-Free Order

AbstractA complete classification is given of finite primitive permutation groups which contain a regular subgroup of square-free order. Then a collection $${\cal P}{\cal N}{\cal C}$$ of square-free numbers n is obtained such that there exists a vertex-primitive non-Cayley graph on n vertices if and only if n is a member of $${\cal P}{\cal N}{\cal C}$$.

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