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Regular orbits of symmetric and alternating groups
Given a nite group G and a faithful irreducible FG-module V where F has prime order, does G have a regular orbit on V ? This problem is equivalent to determining which primitive permutation groups ofExpand
The base size of a primitive diagonal group
Abstract A base B for a finite permutation group G acting on a set Ω is a subset of Ω with the property that only the identity of G can fix every point of B . We prove that a primitive diagonal groupExpand
Stochastic cycle selection in active flow networks
We relate the self-organizing behavior of actively driven flows to the fundamental topological symmetries of the underlying network, resulting in a class of predictive models with applicability across biological scales. Expand
Primitive permutation groups with a suborbit of length 5 and vertex-primitive graphs of valency 5
We classify finite primitive permutation groups having a suborbit of length 5. Expand
Locally triangular graphs and rectagraphs with symmetry
A graph Γ is locally rank 3 if there exists G ⩽ Aut ( Γ ) such that for each vertex u , the permutation group induced by the vertex stabiliser G u on the neighbourhood Γ ( u ) is transitive of rank 3. Expand
Bases of primitive permutation groups
A base B for a finite permutation group G acting on a set Ω is a subset of Ω with the property that only the identity of G can fix every element of B. In this dissertation, we investigate someExpand
Locally triangular graphs and normal quotients of the n-cube
For an integer $$n\ge 2$$n≥2, the triangular graph has vertex set the 2-subsets of $$\{1,\ldots ,n\}$${1,…,n} and edge set the pairs of 2-subsets intersecting at one point. Such graphs are known toExpand
On k-connected-homogeneous graphs
A graph Γ is k-connected-homogeneous (k-CH) if k is a positive integer and any isomorphism between connected induced subgraphs of order at most k extends to an automorphism of Γ, if this property holds for all k. Expand
The O'Nan-Scott Theorem for Finite Primitive Permutation Groups, and Finite Representability
Introduction 11 Preliminaries 31.1 Centralizers and Normalizers . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Group Actions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Expand
Information transmission and signal permutation in active flow networks
Francis G. Woodhouse, ∗ Joanna B. Fawcett, † and Jörn Dunkel Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, U.K. Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge MA 02139-4307, U U.S.A. Expand