Orbits of permutation groups on unordered sets, IV: Homogeneity and transitivity

Peter J. Cameron

doi:10.1112/jlms/s2-27.2.238

Orbits of permutation groups on unordered sets, IV: Homogeneity and transitivity

Peter J. Cameron^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We construct and characterise a 3-homogeneous but not 2-primitive permutation group H of countable degree. It has a transitive extension J which is 5-homogeneous but not 3-primitive; the number n_k(J) of orbits of J on k-sets is the number of boron trees with k end-vertices. Some groups related to other classes of trees are also constructed. An application to the growth rate of (n_k(G)) for primitive groups G is given.

Original language	English
Pages (from-to)	238-247
Number of pages	10
Journal	Journal of the London Mathematical Society
Volume	S2-27
Issue number	2
DOIs	https://doi.org/10.1112/jlms/s2-27.2.238
Publication status	Published - 1 Jan 1983

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AB - We construct and characterise a 3-homogeneous but not 2-primitive permutation group H of countable degree. It has a transitive extension J which is 5-homogeneous but not 3-primitive; the number nk(J) of orbits of J on k-sets is the number of boron trees with k end-vertices. Some groups related to other classes of trees are also constructed. An application to the growth rate of (nk(G)) for primitive groups G is given.

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Orbits of permutation groups on unordered sets, IV: Homogeneity and transitivity

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