Maximal subgroups of the Harada-Norton group. (English) Zbl 0595.20017
In this paper the maximal subgroups of the sporadic simple Harada-Norton group HN are determined. It completes some work of K. Harada [Proc. Conf. Finite Groups, Utah 1975, 119-276 (1976; Zbl 0353.20010)] and S. P. Norton [Ph. D. thesis, Univ. Cambridge (1975)]. This result is also recorded in ”An ATLAS of Finite Groups” (1985; Zbl 0568.20001)]. In this paper the complete proofs are given. The methods in the proof are standard and there is the usual division in the local and nonlocal case. Also use is made of a graph of valence 462 on 1.140.000 nodes on which HN acts.
Reviewer: U.Dempwolff
MSC:
| 20D08 | Simple groups: sporadic groups |
| 20D30 | Series and lattices of subgroups |
| 20E28 | Maximal subgroups |
References:
| [1] | Conway, J. H.; Curti, R. T.; Norton, S. P.; Parker, R. A.; Wilson, R. A., (An ATLAS of Finite Groups (1985), Oxford Univ. Press: Oxford Univ. Press London) · Zbl 0568.20001 |
| [2] | Harada, K., On the simple group \(F\) of order \(2^{14}\) · \(3^6\) · \(5^6\) · 7 · 11 · 19, (Scott, W. R.; Gross, F., Proceedings of the Conference on Finite Groups. Proceedings of the Conference on Finite Groups, Utah 1975 (1976), Academic Press: Academic Press New York), 119-276 |
| [3] | Norton, S. P., \(F\) and Other Simple Groups, (Ph. D. thesis (1975), Univ. of Cambridge: Univ. of Cambridge England) · Zbl 0844.20010 |
| [4] | Norton, S. P., The Uniqueness of the Fischer-Griess Monster, (McKay, J., Finite Groups—Coming of Age. Finite Groups—Coming of Age, Contemporary Mathematics Series, Vol.45 (1985)), 271-285 · Zbl 0577.20013 |
| [5] | Smith, P. E., On Certain Finite Simple Groups, (Ph. D. thesis (1975), Univ. of Cambridge: Univ. of Cambridge England) · Zbl 0348.20015 |
| [6] | Wilson, R. A., Maximal subgroups of automorphism groups of simple groups, J. London Math. Soc., 32, 2, 460-466 (1985), (2) · Zbl 0562.20006 |
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.
