String C-groups of order 1024

Authors

  • Yasushi Gomi Sophia University
  • Mark Loyola Ateneo de Manila University
  • Ma. Louise Antonette De Las Penas Ateneo de Manila University

DOI:

https://doi.org/10.55016/ojs/cdm.v13i1.62475

Keywords:

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

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.

Author Biographies

  • Yasushi Gomi, Sophia University

    Associate Professor, Department of Information and Communication Sciences

  • Mark Loyola, Ateneo de Manila University
    Assistant Professor, Department of Mathematics
  • Ma. Louise Antonette De Las Penas, Ateneo de Manila University
    Professor, Department of Mathematics

References

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Published

2018-01-29

Issue

Vol. 13 No. 1 (2018)

Section

Articles

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