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Analysing Finite Locally s-arc Transitive Graphs
We present a new approach to analysing finite graphs which admit a vertex intransitive group of automorphisms G and are either locally (G, s)-arc transitive for s > 2 or G-locally primitive. Such…
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Factorisations of sporadic simple groups
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Completely Transitive Codes in Hamming Graphs
TLDR
This paper looks at codes in the Hamming Graphs and provides a structure theorem which shows that completely transitive codes are made up of either transitive or nearly complete, completely transitives codes.
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Quasiprimitive Groups with No Fixed Point Free Elements of Prime Order
The paper determines all permutation groups with a transitive minimal normal subgroup that have no fixed point free elements of prime order. All such groups are primitive and are wreath products in a…
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Small Maximal Sum-Free Sets
TLDR
All groups with a maximal (by inclusion) sum-free set of size at most 2 and all of size 3 where there exists a ∈ S such that a / ∈ h S \ {a}i .
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Transitive Permutation Groups Without Semiregular Subgroups
A transitive finite permutation group is called elusive if it contains no nontrivial semiregular subgroup. The purpose of the paper is to collect known information about elusive groups. The main…
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New Constructions of Groups Without Semiregular Subgroups
An elusive permutation group is a transitive permutation group with no fixed point free elements of prime order, or equivalently, no nontrivial semiregular subgroups. We provide several new…
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Point regular groups of automorphisms of generalised quadrangles
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There is no upper bound for the diameter of the commuting graph of a finite group
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On Bounding the Diameter of the Commuting Graph of a Group
The commuting graph of a group $G$ is the simple undirected graph whose vertices are the non-central elements of $G$ and two distinct vertices are adjacent if and only if they commute. It is…
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