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The probability of generating a permutation group

Authors:	Email author" target="_blank">A?Lucchini Email author F?Morini

Institution:	(1) Dipartimento di Matematica, Università di Brescia, Via Valotti 9, 25133 Brescia, Italy

Abstract:	It is well known that a permutation group of degree $n \neq 3$ can be generated by $\frac{n}{2}]$ elements. In this paper we study the asymptotic behavior of the probability of generating a permutation group of degree n with $\frac{n}{2}]$ elements. In particular we prove that if n is large enough and $\frac{n}{2}]$ elements generate a permutation group G of degree n modulo G G ², then almost certainly these elements generate G itself. Received: 2 January 2002

Keywords:	20B05 20F69 20P05
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