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Hasan, Zahid and Lim, Bronson 2016. Symmetric Generation of M22. Communications in Algebra,
Taormina, A. and Wendland, K. 2013. The overarching finite symmetry group of Kummer surfaces in the Mathieu group M 24. Journal of High Energy Physics, Vol. 2013, Issue. 8,
Kilic, Nayil and Rowley, Peter 2012. On the maximal rank of primitive residually connected geometries for <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msub><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mrow><mml:mn>22</mml:mn></mml:mrow></mml:msub></mml:math>. Journal of Algebra, Vol. 362, p. 84.
2012. Algebraic and Stochastic Coding Theory.
Wilson, Robert A. 2011. Conway's group and octonions. Journal of Group Theory, Vol. 14, Issue. 1, p. 1.
Bradley, J. D. and Curtis, R. T. 2010. Symmetric Generation and Existence of McL : 2, the Automorphism Group of the McLaughlin Group. Communications in Algebra, Vol. 38, Issue. 2, p. 601.
Curtis, R.T. and Fairbairn, B.T. 2009. Symmetric representation of the elements of the Conway group <mml:math altimg="si1.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mo>⋅</mml:mo></mml:math>0. Journal of Symbolic Computation, Vol. 44, Issue. 8, p. 1044.
Rowley, Peter 2009. The Chamber Graph of the M24 Maximal 2-Local Geometry. LMS Journal of Computation and Mathematics, Vol. 12, p. 120.
Wilson, Robert A. 2009. Octonions and the Leech lattice. Journal of Algebra, Vol. 322, Issue. 6, p. 2186.
Lawther, R. 2007. 2F-modules, abelian sets of roots and 2-ranks. Journal of Algebra, Vol. 307, Issue. 2, p. 614.
Rowley, Peter and Walker, Louise 2004. On point orbits of the Co2-minimal parabolic geometry. Journal of Combinatorial Theory, Series A, Vol. 107, Issue. 2, p. 263.
Rowley, Peter and Walker, Louise 2004. A 11,707,448,673,375 vertex graph related to the baby monster—I. Journal of Combinatorial Theory, Series A, Vol. 107, Issue. 2, p. 181.
Rowley, Peter 2004. Cross Orbits. LMS Journal of Computation and Mathematics, Vol. 7, p. 219.
Rowley, Peter and Walker, Louise 2004. A 11,707,448,673,375 vertex graph related to the baby monster—II. Journal of Combinatorial Theory, Series A, Vol. 107, Issue. 2, p. 215.
Matsuo, Atsushi and Matsuo, Mika 2000. The Automorphism Group of the Hamming Code Vertex Operator Algebra. Journal of Algebra, Vol. 228, Issue. 1, p. 204.
Parker, Christopher and Rowley, Peter 1997. Amalgams Which Involve Sporadic Simple Groups II. Journal of Algebra, Vol. 193, Issue. 2, p. 492.
Pfeiffer, Gotz 1997. The Subgroups of M24, or How to Compute the Table of Marks of a Finite Group. Experimental Mathematics, Vol. 6, Issue. 3, p. 247.
Vardy, Alexander 1995. A new sphere packing in 20 dimensions. Inventiones Mathematicae, Vol. 121, Issue. 1, p. 119.
Suleiman, Ibrahim A.I. and Wilson, Robert A. 1993. Construction of the Fourfold Cover of the Mathieu Group M22. Experimental Mathematics, Vol. 2, Issue. 1, p. 11.
In this paper, we define M24 from scratch as the subgroup of S24 preserving a Steiner system S(5, 8, 24). The Steiner system is produced and proved to be unique and the group emerges naturally with many of its properties apparent.
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