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The relative fixity of a digraph ▫$\Gamma$▫ is defined as the ratio between the largest number of vertices fixed by a nontrivial automorphism of ▫$\Gamma$▫ and the number of vertices of ▫$\Gamma$▫.We characterize the vertex-primitive digraphs whose relative fixity is at least ▫$1 \over 3$▫, and we s ...

Fix ▫$\varepsilon > 0$▫. We say that a finite group ▫$G$▫ is ▫$\varepsilon$▫-quasirandom if every nontrivial irreducible complex representation of ▫$G$▫ has degree at least ▫$|G|^\varepsilon$▫. In this paper, we give a structure theorem for large ▫$\varepsilon$▫-quasirandom groups, and we completely ...

Let ▫$G$▫ be a transitive permutation group acting on ▫$\Omega$▫. In this paper, we introduce and study the parameter ▫${\mathrm {sep}}(G)$▫, which denotes the size of the smallest set of points ▫$A$▫ such that, for every permutation ▫$g\in G$▫, ▫$A \cap A^g$▫ is nonempty. In particular, we focus on ...