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ASYMPTOTIC RESULTS FOR TRANSITIVE PERMUTATION GROUPS

Published online by Cambridge University Press:  01 March 2000

A. LUCCHINI ,
F. MENEGAZZO  and
M. MORIGI
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
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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 c′such that each soluble transitive permutation group of degree n [ges ] 2 can be generated by [c′ n/ √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
Information
Bulletin of the London Mathematical Society , Volume 32 , Issue 2 , March 2000 , pp. 191 - 195
Copyright
© The London Mathematical Society 2000

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