Orbits of permutation groups on unordered sets, III: Imprimitive groups

Peter J. Cameron

doi:10.1112/jlms/s2-27.2.229

Orbits of permutation groups on unordered sets, III: Imprimitive groups

Peter J. Cameron^*

^*Corresponding author for this work

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

Abstract

This paper studies imprimitive groups G having a finite number n_k(G) of orbits on k-sets for all k. The main results are a formula for n_k(G Wr H) in terms of n_k(G) and a ‘modified cycle index’ of H, and relations between the growth rate of (n_k(G)) and the structure of primitive components of G.

Original language	English
Pages (from-to)	229-237
Number of pages	9
Journal	Journal of the London Mathematical Society
Volume	S2-27
Issue number	2
DOIs	https://doi.org/10.1112/jlms/s2-27.2.229
Publication status	Published - 1 Jan 1983

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title = "Orbits of permutation groups on unordered sets, III: Imprimitive groups",

abstract = "This paper studies imprimitive groups G having a finite number nk(G) of orbits on k-sets for all k. The main results are a formula for nk(G Wr H) in terms of nk(G) and a {\textquoteleft}modified cycle index{\textquoteright} of H, and relations between the growth rate of (nk(G)) and the structure of primitive components of G.",

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year = "1983",

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doi = "10.1112/jlms/s2-27.2.229",

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AU - Cameron, Peter J.

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N2 - This paper studies imprimitive groups G having a finite number nk(G) of orbits on k-sets for all k. The main results are a formula for nk(G Wr H) in terms of nk(G) and a ‘modified cycle index’ of H, and relations between the growth rate of (nk(G)) and the structure of primitive components of G.

AB - This paper studies imprimitive groups G having a finite number nk(G) of orbits on k-sets for all k. The main results are a formula for nk(G Wr H) in terms of nk(G) and a ‘modified cycle index’ of H, and relations between the growth rate of (nk(G)) and the structure of primitive components of G.

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U2 - 10.1112/jlms/s2-27.2.229

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SP - 229

EP - 237

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

IS - 2

ER -

Orbits of permutation groups on unordered sets, III: Imprimitive groups

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