On primitive permutation groups with small suborbits and their orbital graphs.
type: Item
instance of: scholarly article
title: On primitive permutation groups with small suborbits and their orbital graphs.
zbMATH Open document ID: 1069.20004
author: Cai Heng Li
author: Zai Ping Lu
author: Dragan Marušič
published in: Journal of Algebra
publication date: 2004-10-01T00:00:00Z
review text: In the present paper finite primitive permutation groups with a suborbit of length \(4\) or \(3\) are studied as well as vertex-primitive arc-transitive graphs of valency \(3\) or \(4\) and half-arc-transitive vertex-primitive graphs of valency \(2k\) for infinitely many integers \(k\geq 14\). Here a vertex-transitive graph is called half-arc-transitive if its automorphism group acts transitively on the edges but not transitively on the set of ordered pairs of adjacent vertices, called arcs. In particular, the authors establish a precise list of finite permutation groups with a suborbit of length \(4\) and show that the order of a point stabilizer in this case never is \(2^43^6\), contrary to a claim by \textit{W. L. Quirin} [Math. Z. 122, 267-274 (1971; Zbl 0213.03302)]. They also show that there are no half-arc-transitive graphs of valency less than \(10\).
Mathematics Subject Classification ID: 20B15
Mathematics Subject Classification ID: 20B10
Mathematics Subject Classification ID: 20B25
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 2104463
zbMATH Keywords: primitive permutation groups
zbMATH Keywords: vertex-primitive graphs
zbMATH Keywords: arc-transitive graphs
zbMATH Keywords: half-arc-transitive graphs
zbMATH Keywords: subdegrees
zbMATH Keywords: suborbits
zbMATH Keywords: orbitals
zbMATH Keywords: valencies
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2004.03.005
OpenAlex ID: W2036147376
cites work: Vertex and Edge Transitive, but not 1-Transitive, Graphs
cites work: On the Sims Conjecture and Distance Transitive Graphs
cites work: Q3684278
cites work: Vertex-primitive ½-arc-transitive graphs of smallest order
cites work: Primitive Permutationsgruppen mit einem zweifach primitiven Subkonstituenten
cites work: The finite vertex-primitive and vertex-biprimitive \(s\)-transitive graphs for \(s\geq 4\)
cites work: On finite \(s\)-transitive graphs of odd order
cites work: Finite 𝑠-arc transitive Cayley graphs and flag-transitive projective planes
cites work: On half-transitive metacirculant graphs of prime-power order
cites work: A classification of the maximal subgroups of the finite alternating and symmetric groups
cites work: Recent developments in half-transitive graphs
cites work: On the point stabilizers of transitive groups with non-self-paired suborbits of length 2
cites work: Vertex-primitive graphs of order a product of two distinct primes
cites work: Q4161482
cites work: Primitive permutation groups with small orbitals
cites work: Graphs and finite permutation groups. II
cites work: On a class of doubly transitive groups
cites work: Q3926778
cites work: Q5524326
cites work: The primitive permutation groups with an orbital of length 4
cites work: Determination of a class of primitive permutation groups
DOI: 10.1016/J.JALGEBRA.2004.03.005
description: scientific article; zbMATH DE number 2104463