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Building on earlier results for regular maps and for orientably regular chiral maps, we classify the non-abelian finite simple groups arising as automorphism groups of maps in each of the 14 Graver-Watkins classes of edge-transitive maps.
A detailed proof is given of a theorem describing the centraliser of a transitive permutation group, with applications to automorphism groups of objects in various categories of maps, hypermaps, dessins, polytopes and covering spaces, where the autom
In this article we present an extensive survey on the developments in the theory of non-abelian finite groups with abelian automorphism groups, and pose some problems and further research directions.
For a finite group $G$, let $mathrm{diam}(G)$ denote the maximum diameter of a connected Cayley graph of $G$. A well-known conjecture of Babai states that $mathrm{diam}(G)$ is bounded by ${(log_{2} |G|)}^{O(1)}$ in case $G$ is a non-abelian finite si
A family $mathcal L$ of subsets of a set $X$ is called linked if $Acap B eemptyset$ for any $A,Binmathcal L$. A linked family $mathcal M$ of subsets of $X$ is maximal linked if $mathcal M$ coincides with each linked family $mathcal L$ on $X$ that con