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Published online by Cambridge University Press: 01 February 2010
This paper contains a variety of results about the action of Con way‘s largest simple group upon the crosses in the Leech lattice. These results are tailor-made for use in ‘A Monster Graph, I'(Proc. London Math. Soc. (3) 90 (2005) 42-60), where a graph related to the Monster simple group is studied.