Upper bounds on the uniform spreads of the sporadic simple groups

Document Type: Research Paper

Authors

1 Mathematics, Faculty of Science, University of Qom. Qom, Iran

2 Department of Mathematics, Faculty of Science, Iran University of Science & Technology, Tehran, Iran

Abstract

‎‎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.

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