Wilson, Robert A. Every \(\mathrm{PSL}_2(13)\) in the Monster contains \(13A\)-elements. (English) Zbl 1339.20013 LMS J. Comput. Math. 18, 667-674 (2015). The Monster \(M\) is the largest of the 26 finite sporadic simple groups, and the only one whose maximal subgroups are not yet completely classified. Much work has however been done on this problem over the years (see for example the papers of P. E. Holmes and R. A. Wilson [J. Algebra 251, No. 1, 435-447 (2002; Zbl 1006.20015); J. Algebra 319, No. 7, 2653-2667 (2008; Zbl 1146.20009)], S. P. Norton [Lond. Math. Soc. Lect. Note Ser. 249, 198-214 (1998; Zbl 0908.20008)], S. P. Norton and the author [Proc. Lond. Math. Soc., III. Ser. 84, No. 3, 581-598 (2002; Zbl 1017.20009); J. Lond. Math. Soc., II. Ser. 87, No. 3, 943-962 (2013; Zbl 1281.20019)] and the author [LMS J. Comput. Math. 17, 33-46 (2014; Zbl 1297.20014)]), but a few obstinate cases remain. One of these is the problem of classifying subgroups isomorphic to \(\mathrm{PSL}_2(13)\), whose normalizers might be maximal. Norton in the above-mentioned paper described some subgroups isomorphic to \(\mathrm{PSL}_2(13)\) and containing \(13A\)-elements of \(M\). No subgroup in \(M\) isomorphic to \(\mathrm{PSL}_2(13)\) and containing \(13B\)-elements is known. In the given paper, the author shows by conducting an exhaustive computational search that, in fact, no such subgroup exists. Notation of elements here follows the well-known “Atlas of finite groups” (1985; Zbl 0448.20013). Reviewer: Anatoli Kondrat’ev (Ekaterinburg) Cited in 4 Documents MSC: 20D08 Simple groups: sporadic groups 20E28 Maximal subgroups 20-04 Software, source code, etc. for problems pertaining to group theory Keywords:finite simple groups; sporadic simple groups; Monster; maximal subgroups Citations:Zbl 1006.20015; Zbl 1146.20009; Zbl 0908.20008; Zbl 1017.20009; Zbl 1281.20019; Zbl 1297.20014; Zbl 0448.20013 PDFBibTeX XMLCite \textit{R. A. Wilson}, LMS J. Comput. Math. 18, 667--674 (2015; Zbl 1339.20013) Full Text: DOI References: [1] DOI: 10.1016/j.jalgebra.2003.11.014 · Zbl 1146.20009 · doi:10.1016/j.jalgebra.2003.11.014 [2] DOI: 10.1112/S0024610702003976 · Zbl 1065.20026 · doi:10.1112/S0024610702003976 [3] DOI: 10.1006/jabr.2001.9037 · Zbl 1006.20015 · doi:10.1006/jabr.2001.9037 [4] Conway, An atlas of finite groups (1985) [5] Norton, Proceedings of the Atlas Ten Years on Conference, Birmingham, 1995 pp 198– (1998) [6] DOI: 10.1112/S1461157013000247 · Zbl 1297.20014 · doi:10.1112/S1461157013000247 [7] DOI: 10.1007/978-1-84800-988-2 · Zbl 1203.20012 · doi:10.1007/978-1-84800-988-2 [8] DOI: 10.1112/jlms/jds078 · Zbl 1281.20019 · doi:10.1112/jlms/jds078 [9] DOI: 10.1112/S0024611502013357 · Zbl 1017.20009 · doi:10.1112/S0024611502013357 [10] DOI: 10.1007/s000130050437 · Zbl 0956.20022 · doi:10.1007/s000130050437 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.