We study the asymptotic behavior of the probability of generating a finite completely reducible linear group $G$ of degree $n$ with $[\beta n]$ elements. In particular we prove that if $\beta \geq 3/2$ and $n$ is large enough then $[\beta n]$ randomly chosen elements that generate $G$ modulo $\oo(G)$ almost certainly generate $G$ itself.
THE PROBABILITY OF GENERATING A FINITE LINEAR GROUP / Lucchini, A; Morini, Fiorenza. - In: ARCHIV DER MATHEMATIK. - ISSN 0003-889X. - 83:(2004), pp. 394-403. [10.1007/s00013-004-1154-4]
THE PROBABILITY OF GENERATING A FINITE LINEAR GROUP
MORINI, Fiorenza
2004-01-01
Abstract
We study the asymptotic behavior of the probability of generating a finite completely reducible linear group $G$ of degree $n$ with $[\beta n]$ elements. In particular we prove that if $\beta \geq 3/2$ and $n$ is large enough then $[\beta n]$ randomly chosen elements that generate $G$ modulo $\oo(G)$ almost certainly generate $G$ itself.File in questo prodotto:
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