From Higman-Sims to Urysohn: a random walk through groups, graphs, designs, and spaces

نویسنده

  • Peter J. Cameron
چکیده

A better example is the Higman–Sims group. This is a primitive permutation group on 100 points. The point stabiliser is the Mathieu group M22, having orbits of sizes 1, 22 and 77, and acts 3-transitively on its orbit of size 22. Note that 77 = 22 · 21/6, so two points at distance 2 in the orbital graph of valency 22 have six common neighbours. The Higman–Sims group acts transitively on 3claws, on 4-cycles, and on paths of length 3 not contained in 4-cycles. (The graphwas constructed earlier by DaleMesner, who never thought to look at its automorphism group. The group was constructed in a different action by Graham Higman.)

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تاریخ انتشار 2007