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ENUMERATING TRANSITIVE FINITE PERMUTATION GROUPS

Published online by Cambridge University Press:  01 November 1998

ANDREA LUCCHINI
ANDREA LUCCHINI
Affiliation:
Dipartimento di Elettronica per l'Automazione, Università di Brescia, Via Branze, 25123 Brescia, Italy
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Abstract

Denote by f(n) the number of subgroups of the symmetric group Sym(n) of degree n, and by ftrans(n) the number of its transitive subgroups. It was conjectured by Pyber [9] that almost all subgroups of Sym(n) are not transitive, that is, ftrans(n)/f(n) tends to 0 when n tends to infinity. It is still an open question whether or not this conjecture is true. The difficulty comes from the fact that, from many points of view, transitivity is not a really strong restriction on permutation groups, and there are too many transitive groups [9, Sections 3 and 4]. In this paper we solve the problem in the particular case of permutation groups of prime power degree, proving the following result.

Type
Notes and Papers
Information
Bulletin of the London Mathematical Society , Volume 30 , Issue 6 , November 1998 , pp. 569 - 577
Copyright
© The London Mathematical Society 1998

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