The Mathieu GroupM12and Its Pseudogroup ExtensionM13
نویسندگان
چکیده
منابع مشابه
The Mathieu group M12 and its pseudogroup extension M13, Experiment
We study a construction of the Mathieu group M12 using a game reminiscent of Loyd’s “15-puzzle”. The elements of M12 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” M13 acting on all 13 points, which exhibits a limited form of sextuple transitivity. Another corollary of the construction is a metric, a...
متن کاملThe Mathieu Group M 12 and Its Pseudogroup Extension
We study a construction of the Mathieu group M12 using a game reminiscent of Loyd’s “15-puzzle”. The elements of M12 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” M13 acting on all 13 points, which exhibits a limited form of sextuple transitivity. Another corollary of the construction is a metric, a...
متن کاملThe Mathieu Group M 12 and Its Pseudogroup Extension M 13
We study a construction of the Mathieu group M12 using a game reminiscent of Loyd’s “15-puzzle”. The elements of M12 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” M13 acting on all 13 points, which exhibits a limited form of sextuple transitivity. Another corollary of the construction is a metric, a...
متن کاملRing of the Mathieu
We investigate the classical Zassenhaus conjecture for the unit group of the integral group ring of Mathieu simple group M 23 using the Luthar-Passi method. This work is a continuation of the research that we carried out for Mathieu groups M 11 and M 12. As a consequence, for this group we confirm Kimmerle's conjecture on prime graphs.
متن کاملDecoding the Mathieu Group
The sporadic Mathieu group M12 can be viewed as an errorcorrecting code, where the codewords are the group’s elements written as permutations in list form, and with the usual Hamming distance. We investigate the properties of this group as a code, in particular determining completely the probabilities of successful and ambiguous decoding of words with more than 3 errors (which is the number tha...
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ژورنال
عنوان ژورنال: Experimental Mathematics
سال: 2006
ISSN: 1058-6458,1944-950X
DOI: 10.1080/10586458.2006.10128958