The Mathieu group $M_{12}$ and its pseudogroup extension $M_{13}$

Details The Mathieu group $M_{12}$ and its pseudogroup extension $M_{13}$ The Mathieu group $M_{12}$ and its pseudogroup extension $M_{13}$

2005-08-31

arxiv.org/abs/math/0508630v1

Mathematics

Group Theory

19 pages, uses mathrsfs

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

The Mathieu group $M_{12}$ and its pseudogroup extension $M_{13}$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Mathieu group $M_{12}$ and its pseudogroup extension $M_{13}$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Mathieu group $M_{12}$ and its pseudogroup extension $M_{13}$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-116809