New Upper Bounds on the Spreads of Some Large Sporadic Groups
arXiv:0907.2028
Abstract
Let G be a group. We say that G has spread r if for any set of distinct elements {x1,..., xr}\subset G there exists an element y\in G with the property that <xi, y>=G for every 0<i<r+1. Few bounds on the spread of finite simple groups are known. In this paper we present improved upper bounds for the spread of many of the sporadic simple groups, in some cases improving on the best known upper bound by several orders of magnitude.
arXiv commentThis essentially is to appear in Communications of Algebra. This version contains better bounds for the groups M23 and B and also contains some concluding remarks