The Mathieu group M-12 and its pseudogroup extension M-13

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The Mathieu group M-12 and its pseudogroup extension M-13

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Title: The Mathieu group M-12 and its pseudogroup extension M-13
Author: Elkies, Noam; Conway, John H.; Martin, Jeremy L.

Note: Order does not necessarily reflect citation order of authors.

Citation: Conway, 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.
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Abstract: We 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.
Published Version: http://akpeters.metapress.com/content/gl2588q303344231
Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA
Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:2794826

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  • FAS Scholarly Articles [6463]
    Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University
 
 

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