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

Access to Document

10.1112/jlms/s2-27.2.238

Cite this

@article{b50b4c39be384e0f84caa7751b691b52,

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

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 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.",

author = "Cameron, {Peter J.}",

year = "1983",

month = jan,

day = "1",

doi = "10.1112/jlms/s2-27.2.238",

language = "English",

volume = "S2-27",

pages = "238--247",

journal = "Journal of the London Mathematical Society",

issn = "0024-6107",

publisher = "John Wiley & Sons, Ltd",

number = "2",

}

TY - JOUR

T1 - Orbits of permutation groups on unordered sets, IV

T2 - Homogeneity and transitivity

AU - Cameron, Peter J.

PY - 1983/1/1

Y1 - 1983/1/1

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=84959848285&partnerID=8YFLogxK

U2 - 10.1112/jlms/s2-27.2.238

DO - 10.1112/jlms/s2-27.2.238

M3 - Article

AN - SCOPUS:84959848285

SN - 0024-6107

VL - S2-27

SP - 238

EP - 247

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

IS - 2

ER -

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

Abstract

Access to Document

Other files and links

Fingerprint

Cite this