Upper bounds on the uniform spreads of the sporadic simple groups

‎‎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 $s_۱, s_۲,‎\ldots‎,s_k$ in $G$ there exists $y\in C$ such that $G = \langle s_i,y\rangle$ for $i=۱, ۲,‎\ldots,k$‎. ‎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.

Keywords:

‎Exact uniform spread‎ , ‎Exact spread‎ , ‎Sporadic group