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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 results are recursive constructions of elusive permutation groups, using various product operations and affine group constructions. A brief historical introduction(More)
The following problem is considered: if H is a semiregular abelian subgroup of a transitive permutation group G acting on a finite set X, find conditions for (non)existence of G-invariant partitions of X and give their description in terms of orbits of H. Conditions and descriptions presented in this paper are derived by studying spectral properties of the(More)
AIMS To investigate the prevalence of pathological internet use (PIU) and maladaptive internet use (MIU) among adolescents in 11 European countries in relation to demographic, social factors and internet accessibility. DESIGN Cross-sectional survey. SETTING The 7th Framework European Union (EU) funded project, Saving and Empowering Young Lives in Europe(More)
Let p be a prime. It was shown by Folkman (J. Combin. Theory 3 (1967) 215) that a regular edge-transitive graph of order 2p or 2p 2 is necessarily vertex-transitive. In this paper an extension of his result in the case of cubic graphs is given. It is proved that, with the exception of the Gray graph on 54 vertices, every cubic edge-transitive graph of order(More)
In this paper we study finite, connected, 4-valent graphs X which admit an action of a group G which is transitive on vertices and edges, but not transitive on the arcs of X. Such a graph X is said to be (G, 1Â2)-transitive. The group G induces an orientation of the edges of X, and a certain class of cycles of X (called alternating cycles) determined by the(More)