GAP (CTblLib) - References

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[ABC] Improvements to the ATLAS of Brauer Characters, The MOC Group, https://www.math.rwth-aachen.de/homes/MOC/ABCerr.html.

[BGL+10] Breuer, T., Guralnick, R. M., Lucchini, A., Maróti, A. and Nagy, G. P., Hamiltonian cycles in the generating graphs of finite groups, Bull. London Math. Soc., 42 (4) (2010), 621–633.

[BL23] Breuer, T. and Lübeck, F., Browse, ncurses interface and browsing applications, Version 1.8.21 (2023)
(GAP package), https://www.math.rwth-aachen.de/~Browse.

[BMO17] Breuer, T., Malle, G. and O'Brien, E. A., Reliability and reproducibility of Atlas information, in Finite simple groups: thirty years of the atlas and beyond, Amer. Math. Soc., Contemp. Math., 694, Providence, RI (2017), 21–31.

[BMW20] Breuer, T., Magaard, K. and Wilson, R. A., Verification of the ordinary character table of the Baby Monster, J. Algebra, 561 (2020), 111–130.

[BMW24] Breuer, T., Magaard, K. and Wilson, R. A., Verification of the conjugacy classes and ordinary character table of the Monster (2024), submitted.

[BN95] Breuer, T. and Norton, S. P., Improvements to the Atlas, The Clarendon Press Oxford University Press, London Mathematical Society Monographs. New Series, 11, New York (1995), 297–327
(Appendix 2 by T. Breuer and S. Norton, Oxford Science Publications).

[Bos90] Bosma, W., Canonical bases for cyclotomic fields, Appl. Algebra Engrg. Comm. Comput., 1 (2) (1990), 125–134.

[Brea] Breuer, T., Ambiguous Class Fusions in the GAP Character Table Library, https://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc2/manual.pdf.

[Breb] Breuer, T., Constructing Character Tables of Central Extensions in GAP, https://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc2/manual.pdf.

[Brec] Breuer, T., Constructing the ordinary character tables of some Atlas groups using character theoretic methods., arXiv:1604.00754.

[Bred] Breuer, T., Permutation Characters in GAP, https://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc2/manual.pdf.

[Bree] Breuer, T., GAP computations concerning probabilistic generation of finite simple groups, arXiv:0710.3267.

[Bref] Breuer, T., Using Table Automorphisms for Constructing Character Tables in GAP, https://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc2/manual.pdf.

[Bre11] Breuer, T., Computing character tables of groups of type \(M.G.A\), LMS J. Comput. Math., 14 (2011), 173–178.

[CCN+85] Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A. and Wilson, R. A., Atlas of finite groups, Oxford University Press, Eynsham (1985), xxxiv+252 pages
(Maximal subgroups and ordinary characters for simple groups, With computational assistance from J. G. Thackray).

[Cla05] Claßen-Houben, M., Jordan-Zerlegung der Charaktere für die GAP-Charaktertafeln der endlichen Gruppen vom Lie-Typ, Diplomarbeit, Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule, Aachen, Germany (2005).

[CP96] Cannon, J. J. and Playoust, C., An introduction to algebraic programming in Magma, School of Mathematics and Statistics, University of Sydney, Sydney, Australia (1996), http://www.math.usyd.edu.au:8000/u/magma.

[Dan06] Dany, S., Berechnung von Charaktertafeln zentraler Erweiterungen ausgewählter Gruppen, Diplomarbeit, Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule, Aachen, Germany (2006).

[DLP25] Dietrich, H., Lee, M. and Popiel, T., The maximal subgroups of the Monster (2025), Advances in Mathematics 469 (2025), article 110214.

[DLPP24] Dietrich, H., Lee, M., Pisani, A. and Popiel, T., Explicit construction of the maximal subgroups of the Monster (2024), arXiv:2411.12230.

[GAP24] GAP – Groups, Algorithms, and Programming, Version 4.13.1, The GAP Group (2024), https://www.gap-system.org.

[GR] Guralnick, R. M. and Robinson, G. R., Commuting involutions and elementary abelian subgroups of simple groups, arXiv:2012.08693.

[Han88] Hanrath, W., Irreduzible Darstellungen von Raumgruppen, Dissertation, Rheinisch Westfälische Technische Hochschule, Aachen, Germany (1988).

[HJLP] Hiss, G., Jansen, C., Lux, K. and Parker, R. A., Computational Modular Character Theory, http://www.math.rwth-aachen.de/~MOC/CoMoChaT/.

[HP89] Holt, D. F. and Plesken, W., Perfect groups, The Clarendon Press Oxford University Press, Oxford Mathematical Monographs, New York (1989), xii+364 pages
(With an appendix by W. Hanrath, Oxford Science Publications).

[JLPW95] Jansen, C., Lux, K., Parker, R. and Wilson, R., An atlas of Brauer characters, The Clarendon Press Oxford University Press, London Mathematical Society Monographs. New Series, 11, New York (1995), xviii+327 pages
(Appendix 2 by T. Breuer and S. Norton, Oxford Science Publications).

[LN18] Lübeck, F. and Neunhöffer, M., GAPDoc, A Meta Package for GAP Documentation, Version 1.6.2 (2018)
(GAP package), https://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc.

[LOST10] Liebeck, M. W., O'Brien, E. A., Shalev, A. and Tiep, P. H., The Ore conjecture, J. Eur. Math. Soc. (JEMS), 12 (4) (2010), 939–1008.

[LP91] Lux, K. and Pahlings, H. (Michler, G. O. and Ringel, C. M., Eds.), Computational aspects of representation theory of finite groups, in Representation theory of finite groups and finite-dimensional algebras (Bielefeld, 1991), Birkhäuser, Progr. Math., 95, Basel (1991), 37–64.

[LP10] Lux, K. and Pahlings, H., Representations of groups, Cambridge University Press, Cambridge Studies in Advanced Mathematics, 124, Cambridge (2010), x+460 pages
(A computational approach).

[MNP19] Merkwitz, T., Naughton, L. and Pfeiffer, G., TomLib, The GAP Library of Tables of Marks, Version 1.2.9 (2019)
(GAP package), https://gap-packages.github.io/tomlib.

[Nav98] Navarro, G., Characters and blocks of finite groups, Cambridge University Press, London Mathematical Society Lecture Note Series, 250, Cambridge (1998), x+287 pages.

[Noe02] Noeske, F., Zur Darstellungstheorie der Schurschen Erweiterungen symmetrischer Gruppen, Diplomarbeit, Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule (2002).

[Nor] Norton, S. P., Improvements to the ATLAS–II, http://brauer.maths.qmul.ac.uk/Atlas/info/fullatlasmods.html.

[NPP84] Neubüser, J., Pahlings, H. and Plesken, W. (Atkinson, M. D., Ed.), CAS; design and use of a system for the handling of characters of finite groups, in Computational group theory (Durham, 1982), Academic Press, London (1984), 195–247.

[Ost86] Ostermann, T., Charaktertafeln von Sylownormalisatoren sporadischer einfacher Gruppen, Universität Essen, Universität Essen Fachbereich Mathematik, Vorlesungen aus dem Fachbereich Mathematik der Universität GH Essen [Lecture Notes in Mathematics at the University of Essen], 14, Essen (1986), x+187 pages.

[Pis25] Pisani, A., Computing the Character Table of a 2-local Maximal Subgroup of the Monster (2025), arXiv:2503.15857.

[PP24] Pisani, A. and Popiel, T., Conjugacy class fusion from four maximal subgroups of the Monste (2024), arXiv:2404.05194.

[WPN+22] Wilson, R. A., Parker, R. A., Nickerson, S., Bray, J. N. and Breuer, T., AtlasRep, A GAP Interface to the Atlas of Group Representations, Version 2.1.6 (2022)
(GAP package), https://www.math.rwth-aachen.de/~Thomas.Breuer/atlasrep.

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