Base sizes of primitive groups: bounds with explicit constants
File(s)base-with-constants-HLM3.pdf (464.51 KB)
Accepted version
Author(s)
Liebeck, Martin
Halasi, Zoltan
Maroti, Attila
Type
Journal Article
Abstract
We show that the minimal base size b(G) of a finite primitive permutation
group G of degree n is at most 2(log|G|/logn)+ 24. This bound is asymptotically best possible since there exists a sequence of primitive
permutation groups G of degrees n such that b(G)= 2(log|G|/log n) − 2
and b(G) is unbounded. As a corollary we show that a primitive permutation group of degree n that does not contain the alternating
group Alt(n) has a base of size at most max {√n,25}.
group G of degree n is at most 2(log|G|/logn)+ 24. This bound is asymptotically best possible since there exists a sequence of primitive
permutation groups G of degrees n such that b(G)= 2(log|G|/log n) − 2
and b(G) is unbounded. As a corollary we show that a primitive permutation group of degree n that does not contain the alternating
group Alt(n) has a base of size at most max {√n,25}.
Date Issued
2019-03-01
Date Acceptance
2018-11-29
Citation
Journal of Algebra, 2019, 521, pp.16-43
ISSN
0021-8693
Publisher
Elsevier
Start Page
16
End Page
43
Journal / Book Title
Journal of Algebra
Volume
521
Copyright Statement
© 2018 Elsevier Inc. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence http://creativecommons.org/licenses/by-nc-nd/4.0/
Subjects
Science & Technology
Physical Sciences
Mathematics
Minimal base size
Primitive permutation group
Classical group
Irreducible linear group
PERMUTATION-GROUPS
FINITE
CONJECTURE
ORDERS
0101 Pure Mathematics
General Mathematics
Publication Status
Published
Date Publish Online
2018-11-30