×

zbMATH — the first resource for mathematics

The classes and representations of the groups of 27 lines and 28 bitangents. (English) Zbl 0045.00505

Keywords:
Group theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] H. F. Baker,A locus with 25920 self transformations, Cambridge University Press, 1946. · Zbl 0063.00170
[2] Brahana, H. R., Generators of known simple groups, Annals of Math., 31, 2, 529-549 (1930) · JFM 56.0131.03
[3] R. Brauer andC. Nesbitt,On the modular representations of groups of finite order, University of Toronto studies, Mathematical Series n. 4, 1937. · Zbl 0018.29504
[4] Brauer, R.; Nesbitt, C., On the modular characters of groups, Annals of Math., 42, 2, 556-590 (1941) · JFM 67.0073.02
[5] Brauer, R., On groups whose order contains a prime number to the first power, Amer. Journal of Math., LXIV, 2, 401-420 (1942) · Zbl 0061.03703
[6] Burkhardt, H., Untersuchungen aus dem Gebiete der hyperelliptischen Modulfunctionen, Math. Annalen, 38, 161-224 (1891) · JFM 23.0490.01
[7] Burkhardt, H., Untersuchungen aus dem Gebiete der hyperelliptischen Modulfunctionen, Math. Annalen, 41, 313-343 (1893) · JFM 24.0465.02
[8] Cartan, E., La géometrie des groupes simples, Annali di Matematica pura ed applicata, 4, 209-256 (1927) · JFM 53.0392.03
[9] Coxeter, H. S. M., The pure archimedean polytopes in six and seven dimensions, Proc. Camb. Phil. Soc., 24, 1-9 (1928) · JFM 54.0648.02
[10] Coxeter, H. S. M., The polytopes with regular-prismatic vertex figures, Phil. Trans. Roy. Soc. London, 229, 329-425 (1930) · JFM 56.1119.03
[11] Coxeter, H. S. M., The polytopes with regular-prismatic vertex figures, Proc. London Math. Soc., 34, 2, 126-189 (1932) · JFM 58.1212.02
[12] Coxeter, H. S. M., Finite groups generated by reflections and their subgroups generated by reflections, Proc. Camb. Phil. Soc-., 50, 466-482 (1934) · JFM 60.0898.04
[13] Coxeter, H. S. M., The polytope 2_21,whose 27 vertices correspond to the lines on the general cubic surface, Amer. Journ. of Math., 62, 457-486 (1940) · JFM 66.0769.02
[14] Coxeter, H. S. M., Regular polytopes (1948), London: Methuen and Co., London · Zbl 0031.06502
[15] L. E. Dickson,Linear groups, with an exposition of Galois field theory, Leipzig 1901. · JFM 32.0128.01
[16] Frame, J. S., The simple group of order 25920, Duke Math. Journ., 2, 477-484 (1936) · Zbl 0015.00505
[17] Frame, J. S., A symmetric representation of the twenty-seven lines on a cubic surface by lines in a finite geometry, Bull. Amer. Math. Soc., 44, 658-661 (1938) · JFM 64.0697.02
[18] Frame, J. S., Congruence relations between the traces of matrix powers, Canadian Journal of Math., 1, 3, 303-304 (1949) · Zbl 0041.15205
[19] Frobenius, G., Ueber die Beziehungen zwischen den 28 Doppeltangenten einer ebenen Curve vierter Ordnung, Journal für Math., 99, 276-276 (1886) · JFM 18.0696.01
[20] Geiser, C. F., Ueber die Doppeltangenten einer ebenen Curve vierten Grades, Math. Annalen, 1, 129-129 (1869) · JFM 02.0417.01
[21] Gosset, T., On the regular and semi-regular figures in space of n-dimensions, Messenger of Mathematics, 24, 43-48 (1900)
[22] Jordan, C., Sur la trisection des fonctions abéliennes et sur les vingt-sept droites des surfaces du troisième ordre, Comptes Rendus, LXVIII, 865-869 (1869) · JFM 02.0331.03
[23] A. Henderson,The twenty-seven lines upon a cubic surface, Cambridge 1911. · JFM 42.0661.01
[24] Hesse, O., Ueber die Doppeltangenten einer ebenen Curve vierter Ordnung, Journal für Math., 49, 279-279 (1855)
[25] Klein, F., Sur la résolution, par des fonctions hyperelliptiques, de l’équation du vingtseptième degré, de laquelle depend la determination des vingt-sept droites d’une surface cubique, Journal de Math., 4, 169-176 (1888) · JFM 20.0816.01
[26] Littlewood, D. E., The theory of group characters (1940), Oxford: Clarendon Press, Oxford · JFM 66.0093.02
[27] Maschke, H., Aufstellung des vollen Formensystems einer quaternären Gruppe von 51840 linearen Substitutionen, Math. Annalen, 33, 317-344 (1888) · JFM 21.0142.03
[28] Racah, G., Sulla caratterizzazione delle rappresentazioni irriducibili dei gruppi semisemplici di Lie, Rendiconti dell’Acc. Naz. dei Lincei, VIII, 108-112 (1950) · Zbl 0036.15601
[29] Schoute, P., On the relation between the vertices of a definite six-dimensional polytope and the lines of a cubic surface, Proc. of Sec. of Sci., 13, 375-383 (1910)
[30] Schur, I., Ueber die rationalen Darstellungen der allgemeinen linearen Gruppe, 58-75 (1927), Berlin: Sitzungsber, Berlin · JFM 53.0108.05
[31] Segre, B., Quartiche piane e superficie cubiche, Boll. della Unione Matematica Italiana, 8, 203-210 (1929) · JFM 55.1005.03
[32] Segre, B., The non singular cubic surfaces (1942), Oxford: Clarendon Press, Oxford · JFM 68.0358.01
[33] Todd, J. A., On a quartic primal with forty-five nodes, in space of four dimensions, Quarterly Journal Math., 7, 168-174 (1936) · JFM 62.0789.04
[34] Todd, J. A., On the simple group of order 25920, Proc. Roy. Soc. London, 189, 326-358 (1947) · Zbl 0029.00402
[35] Van Der Waerden, B. L., Die Klassification der einfachen Lieschen Gruppen, Math. Zeitsch., 37, 446-462 (1933) · Zbl 0007.29201
[36] Weyl, H., Theorie der Darstellung kontinuerlicher halb-einfacher Gruppen durch lineare Transformation II, Math. Zeitsch., 24, 328-376 (1926)
[37] A. Witting,Ueber eine Hesse’schen Configuration der ebenen Curve dritter Ordnung analoge Configurationen in Raume, auf welche die Transformationstheorie der hyperelliptischen Functionen (p=2)führt, Dresden 1887. · JFM 18.0765.01
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.