The Mathieu group M-12 and its pseudogroup extension M-13
Conway, John H.
Martin, Jeremy L.
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CitationConway, John H., Noam D. Elkies, and Jeremy L. Martin. 2006. The Mathieu group M-12 and its pseudogroup extension M-13. Experimental Mathematics 15, (2): 223-236.
AbstractWe study a construction of the Mathieu group M-12 using a game reminiscent of Loyd's "15-puzzle." The elements of M-12 are realized as permutations on 12 of the 13 points of the finite projective plane of order 3. There is a natural extension to a "pseudogroup" M-13 acting on all 13 points, which exhibits a limited form of sextuple transitivity. Another corollary of the construction is a metric, akin to that induced by a Cayley graph, on both M-12 and M-13. We develop these results, and extend them to the double covers and automorphism groups of M-12 and M-13, using the ternary Golay code and 12 x 12 Hadamard matrices. In addition, we use experimental data on the quasi-Cayley metric to gain some insight into the structure of these groups and pseudogroups.
Citable link to this pagehttp://nrs.harvard.edu/urn-3:HUL.InstRepos:2794826
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