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تسجيل مستخدم جديدSharp upper bounds on the minimal number of elements required to generate a transitive permutation group
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Gareth Tracey
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The purpose of this paper is to prove that if $G$ is a transitive permutation group of degree $ngeq 2$, then $G$ can be generated by $lfloor cn/sqrt{log{n}}rfloor$ elements, where $c:=sqrt{3}/2$. Owing to the transitive group $D_8circ D_8$ of degree $8$, this upper bound is best possible. Our new result improves a 2018 paper by the author, and makes use of the recent classification of transitive groups of degree $48$.
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