Published 30 Mar 2007. First received 12 Jun 2006.

Improved bounds for the spread of sporadic groups

J. D. Bradley and P. E. Holmes

Abstract: The spread of a group G is the greatest number r such that, for every set of non-trivial elements {x₁,…, x_r}, there exists an element y with the property that < x_i, y > = G for 1 ≤ i ≤ r. In this paper the authors obtain good upper bounds for the spread of fourteen sporadic simple groups computationally, and they determine the value of the spread of M₁₁ by hand.

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Appendix A : This appendix contains the programs used to generate the results presented in the paper, together with the seeds used by MAGMA's random processes to give the exact results.

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