The Mathieu group $M_{12}$ and its pseudogroup extension $M_{13}$
| dc.creator | Conway, John H. | |
| dc.creator | Elkies, Noam D. | |
| dc.creator | Martin, Jeremy L. | |
| dc.date | 2005-08-31 | |
| dc.date.accessioned | 2026-07-07T05:22:49Z | |
| dc.date.available | 2026-07-07T05:22:49Z | |
| dc.description | 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. | |
| dc.description | 19 pages, uses mathrsfs | |
| dc.identifier | https://arxiv.org/abs/math/0508630 | |
| dc.identifier | http://arxiv.org/abs/math/0508630 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76210 | |
| dc.subject | Group Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 20B25 (Primary); 05B25, 51E20, 20B20 (Secondary) | |
| dc.title | The Mathieu group $M_{12}$ and its pseudogroup extension $M_{13}$ | |
| dc.type | text |