Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study a construction of the Mathieu group M12 using a game reminiscent of Loyd's \15-puzzle". The elements of M12 are realized as permu- tations on 12 of the 13 points of the nite projective plane of order 3. There is a natural extension to a \pseudogroup" M13 acting on all 13 points, which exhibits a limited form of sextuple transitivity. Another corollary of the con- struction is a metric, akin to that induced by a Cayley graph, on both M12 and M13.  develop these results, and extend them to the double covers and automorphism groups of M12 and M13, using the ternary Golay code and 12 12 Hadamard matrices. In addition,  use experimental data on the quasi-Cayley metric to gain some insight into the structure of these groups and pseudogroups.
['John H. Conway', 'Noam D. Elkies', 'Jeremy L. Martin']
I am writing a research paper on a idea THE MATHIEU GROUP M12 AND ITS PSEUDOGROUP EXTENSION M13
[{"from": "human", "value": "I am writing a research paper on a idea THE MATHIEU GROUP M12 AND ITS PSEUDOGROUP EXTENSION M13"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study a construction of the Mathieu group M12 using a game reminiscent of Loyd's \\15-puzzle\". The elements of M12 are realized as permu- tations on 12 of the 13 points of the nite projective plane of order 3. There is a natural extension to a \\pseudogroup\" M13 acting on all 13 points, which exhibits a limited form of sextuple transitivity. Another corollary of the con- struction is a metric, akin to that induced by a Cayley graph, on both M12 and M13.  develop these results, and extend them to the double covers and automorphism groups of M12 and M13, using the ternary Golay code and 12 12 Hadamard matrices. In addition,  use experimental data on the quasi-Cayley metric to gain some insight into the structure of these groups and pseudogroups."}]