Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-26T14:05:43.204Z Has data issue: false hasContentIssue false

ASYMPTOTIC RESULTS FOR TRANSITIVE PERMUTATION GROUPS

Published online by Cambridge University Press:  01 March 2000

A. LUCCHINI
Affiliation:
Dipartimento di Elettronica per l'Automazione, Università di Brescia, Via Branze, 25123 Brescia, Italy
F. MENEGAZZO
Affiliation:
Dipartimento di Matematica Pura ed Applicata, Università di Padova, Via Belzoni n.7, 35131 Padova, Italy
M. MORIGI
Affiliation:
Dipartimento di Matematica Pura ed Applicata, Università di Padova, Via Belzoni n.7, 35131 Padova, Italy
Get access

Abstract

In this paper we give answers to some open questions concerning generation and enumeration of finite transitive permutation groups. In [1], Bryant, Kovács and Robinson proved that there is a number csuch that each soluble transitive permutation group of degree n [ges ] 2 can be generated by [cn/ √log n] elements, and later A. Lucchini [5] extended this result (with a different constant c′) to finite permutation groups containing a soluble transitive subgroup. We are now able to prove this theorem in full generality, and this solves the question of bounding the number of generators of a finite transitive permutation group in terms of its degree. The result obtained is the following.

Type
NOTES AND PAPERS
Copyright
© The London Mathematical Society 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)