Orbital diameters of the symmetric and alternating groups
File(s)10.1007%2Fs10801-016-0719-1.pdf (685.82 KB)
Published version
Author(s)
Sheikh, A
Type
Journal Article
Abstract
For a primitive group G acting on a finite set , we define the orbital
diameter to be the maximum of the diameters of all orbital graphs of G. In this paper,
we study the orbital diameters of symmetric and alternating groups. We give necessary
numerical conditions for the orbital diameter to be bounded by some constant c and
give precise descriptions of the actions for which the orbital diameter is bounded by 5.
For each primitive action, we also either determine all orbital graphs of diameter 2 or
give descriptions of infinite families of orbital graphs of diameter 2.
diameter to be the maximum of the diameters of all orbital graphs of G. In this paper,
we study the orbital diameters of symmetric and alternating groups. We give necessary
numerical conditions for the orbital diameter to be bounded by some constant c and
give precise descriptions of the actions for which the orbital diameter is bounded by 5.
For each primitive action, we also either determine all orbital graphs of diameter 2 or
give descriptions of infinite families of orbital graphs of diameter 2.
Date Issued
2016-11-11
Date Acceptance
2016-09-29
Citation
Journal of Algebraic Combinatorics, 2016, 45 (1), pp.1-32
ISSN
0925-9899
Publisher
Springer Verlag
Start Page
1
End Page
32
Journal / Book Title
Journal of Algebraic Combinatorics
Volume
45
Issue
1
Copyright Statement
© The Author(s) 2016. This article is published with open access at Springerlink.com
Subjects
0101 Pure Mathematics
General Mathematics
Publication Status
Published
OA Location
https://link.springer.com/article/10.1007/s10801-016-0719-1
Date Publish Online
2016-11-11