On orbit equivalent permutation groups
type: Item
instance of: scholarly article
title: On orbit equivalent permutation groups
zbMATH Open document ID: 0545.20001
DOI: 10.1007/BF01196650
author: Nicholas F. J. Inglis
published in: Archiv der Mathematik
publication date: 1984-01-01T00:00:00Z
review text: The author gives a proof, independent of the classification of the finite simple groups, of a theorem of A. Wagner that shows there are but seven exceptions to the statement: If two primitive groups acting on the same set X have the same orbits on \(2^ X\) and one is contained in the other, then they are equal. The author states that Siemons and Wagner have independently given such a proof.
Mathematics Subject Classification ID: 20B05
Mathematics Subject Classification ID: 20B15
zbMATH DE Number: 3867548
zbMATH Keywords: primitive groups
zbMATH Keywords: orbits
MaRDI profile type: Publication
cites work: Set-Transitive Permutation Groups
cites work: Q4141385
cites work: An Interchange Property in Finite Permutation Groups
cites work: On groups with no regular orbits on the set of subsets
cites work: \(k\)-homogeneous groups
cites work: Transitivity of finite permutation groups on unordered sets
cites work: On finite permutation groups with the same orbits on unordered sets
cites work: Q5512231
full work available at URL: https://doi.org/10.1007/bf01196650
OpenAlex ID: W2075421912
description: scientific article; zbMATH DE number 3867548