×

Finite quaternionic reflection groups. (English) Zbl 0433.20035


MSC:

20G20 Linear algebraic groups over the reals, the complexes, the quaternions
20H15 Other geometric groups, including crystallographic groups
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Benard, M., Schur indices and splitting fields of the unitary reflection groups, J. Algebra, 38, 318-342 (1976) · Zbl 0327.20004
[2] Blichfeldt, H. F., Finite Collineation Groups (1917), Univ. of Chicago Press: Univ. of Chicago Press Chicago, Ill · JFM 32.0160.01
[3] Bourbaki, N., Groupes et Algèbres de Lie (1968), Hermann: Hermann Paris, Chaps. IV, V, VI · Zbl 0186.33001
[4] Cohen, A. M., Finite complex reflection groups, Ann. Sci. École Norm. Sup., 4, 379-436 (1976), t. 9 · Zbl 0359.20029
[5] Coxeter, H. S.M, Regular Complex Polytopes (1974), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 0296.50009
[6] Crowe, D. W., A regular quaternion polygon, Canad. Math. Bull., 2, 77-79 (1959) · Zbl 0092.13905
[7] Dornhoff, L., Group Representation Theory (1972), Dekker: Dekker New York, Part A · Zbl 0236.20004
[8] Du Val, P., Homographies, Quaternions and Rotations (1964), Clarendon Press: Clarendon Press Oxford · Zbl 0128.15403
[9] Feit, W., The current situation in the theory of finite simple groups, (Actes, Congr. Int. Math., 1 (1970)), 55-93
[10] Gorenstein, D., Finite Groups (1968), Benjamin: Benjamin New York · Zbl 0185.05701
[12] Huffman, W. C., Linear groups containing an element with an eigenspace of codimension two, J. Algebra, 34, 260-287 (1975) · Zbl 0302.20037
[13] Huffman, W. C.; Wales, D. B., Linear groups of degree \(n\) containing an element with exactly \(n\) − 2 equal eigenvalues, Linear and Multilinear Algebra, 3, 53-59 (1975) · Zbl 0326.20038
[14] Huffman, W. C.; Wales, D. B., Linear groups containing an element with an eigenspace of codimension two, (Proceedings of the Conference on Finite Groups (1976), Academic Press: Academic Press New York) · Zbl 0364.20046
[15] Huffman, W. C.; Wales, D. B., Linear groups containing an involution with two eigenvalues — 1, J. Algebra, 45, 465-515 (1977) · Zbl 0364.20046
[16] Serre, J.-P, Représentations linéaires des Groupes finis (1967), Hermann: Hermann Paris
[17] Shephard, G. C.; Todd, J. A., Finite unitary reflection groups, Canad. J. Math., 6, 274-304 (1954) · Zbl 0055.14305
[18] Springer, T. A., Invariant Theory, (Lecture Notes in Mathematics No. 585 (1977), Springer-Verlag: Springer-Verlag Berlin) · Zbl 0346.20020
[19] Steinberg, R., Differential equations invariant under finite reflection groups, Trans. Amer. Math. Soc., 112, 392-400 (1964) · Zbl 0196.39202
[20] Wales, D. B., Linear groups of degree \(n\) containing an involution with two eigenvalues — I, II, J. Algebra, 53, 58-67 (1978) · Zbl 0404.20034
[21] Wiegmann, N. A., Some theorems on matrices with real quaternion elements, Canad. J. Math., 7, 191-201 (1955) · Zbl 0064.01604
[22] Wielandt, H., Finite Permutation Groups (1964), Academic Press: Academic Press New York · Zbl 0138.02501
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.