String C-groups of order 1024

Yasushi Gomi, Mark Loyola, Ma. Louise Antonette De Las Penas

Abstract


This paper determines the non-degenerate string C-groups of order
1024. For groups of rank 3, we use the technique of central extension of
string C-groups of order 512. For groups of rank at least 4, we compute for
quotients of universal string C-groups.

Keywords


string C-groups, abstract regular polytopes, order 1024, 2-groups

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References


M. Conder, Regular polytopes with up to 2000 flags, https://www.math.auckland.ac.nz/ conder/ (2012)

M. Conder, D. Oliveros, The intersection condition for regular polytopes, J. Combin. Theory Ser. A, 120, 1291-1304 (2013)

T. Connor, D. Leemans, C-groups of Suzuki type, J. Algebr. Comb., 42, 849-860 (2015)

M.E. Fernandes, D. Leemans, Polytopes of high rank for the symmetric groups, Adv. Math., 228, 3207-3222 (2011)

M.E. Fernandes, D. Leemans, M. Mixer, Polytopes of high rank for the alternating groups, J. Combin. Theory Ser. A , 119, 42-56 (2012)

The GAP Group, GAP { Groups, Algorithms, and Programming, Version 4.7.8, http://www.gap-system.org (2015)

M.I. Hartley, An atlas of small regular abstract polytopes, Period. Math. Hungar., 53(12), 149-156 (2006)

M.I. Hartley, A. Hulpke, Polytopes derived from sporadic simple groups, Contributions to discrete mathematics, 5(2), 106-118 (2010)

J. Humphreys, Reflection groups and Coxeter groups, Cambridge Studies in Advanced Mathematics 29, Cambridge University Press, Cambridge (1990)

D. Leemans, Almost simple groups of Suzuki type acting on polytopes, Proc. Amer. Math. Soc., 134(12), 3649-3651 (2006)

Computational Algebra Group (University of Sydney), The Magma Computational Algebra System, http://magma.maths.usyd.edu.au/magma/ (2016)

P. McMullen, E. Schulte, Abstract Regular Polytopes, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge (2002)

P. McMullen, E. Schulte, Regular polytopes from twisted Coxeter groups and unitary reflexion groups, Adv. Math., 82, 35-87 (1990)

E. Schulte, A.I. Weiss, Problems on polytopes, their groups, and realizations, Period. Math. Hungar., 53(1-2), 231-255 (2006)




Contributions to Discrete Mathematics. ISSN: 1715-0868