Document Type: Research Paper
Mathematics, Faculty of Science, University of Qom. Qom, Iran
Department of Mathematics, Faculty of Science, Iran University of Science & Technology, Tehran, Iran
A finite group $G$ has uniform spread $k$ if there exists a fixed conjugacy class $C$ of elements in $G$ with the property that for any $k$ nontrivial elements $s_1, s_2,\ldots,s_k$ in $G$ there exists $y\in C$ such that $G = \langle s_i,y\rangle$ for $i=1, 2,\ldots,k$. Further, the exact uniform spread of $G$ is the largest $k$ such that $G$ has the uniform spread $k$. In this paper we give upper bounds on the exact uniform spreads of thirteen sporadic simple groups.