Geodesic
Hurwitz Groups and G2(q)
Canadian mathematical bulletin, Tome 33 (1990) no. 3, pp. 349-357

Voir la notice de l'article provenant de la source Cambridge University Press

Finite factor groups of are called Hurwitz groups. Here we prove that apart from 2G2(3), G2(2), G2(3) and G2(4), all the groups 2G2(32n+1) and G2(q), q = pn, p € P, are Hurwitz groups. For the proof, (2, 3, 7) structure constants are calculated from the character tables [2], [7], and then with the lists of maximal subgroups [8], [5], the existence of generating triples is deduced.
DOI : 10.4153/CMB-1990-059-8
Mots-clés : 20F05, 30F35 
Malle, Gunter. Hurwitz Groups and G2(q). Canadian mathematical bulletin, Tome 33 (1990) no. 3, pp. 349-357. doi: 10.4153/CMB-1990-059-8
@article{10_4153_CMB_1990_059_8,
     author = {Malle, Gunter},
     title = {Hurwitz {Groups} and {G2(q)}},
     journal = {Canadian mathematical bulletin},
     pages = {349--357},
     year = {1990},
     volume = {33},
     number = {3},
     doi = {10.4153/CMB-1990-059-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1990-059-8/}
}
TY  - JOUR
AU  - Malle, Gunter
TI  - Hurwitz Groups and G2(q)
JO  - Canadian mathematical bulletin
PY  - 1990
SP  - 349
EP  - 357
VL  - 33
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1990-059-8/
DO  - 10.4153/CMB-1990-059-8
ID  - 10_4153_CMB_1990_059_8
ER  - 
%0 Journal Article
%A Malle, Gunter
%T Hurwitz Groups and G2(q)
%J Canadian mathematical bulletin
%D 1990
%P 349-357
%V 33
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1990-059-8/
%R 10.4153/CMB-1990-059-8
%F 10_4153_CMB_1990_059_8

[1] 1. Chang, B., The conjugate classes of Chevalley groups of type (G), J. Algebra 9 (1968), pp. 190–211. Google Scholar

[2] 2. Chang, B., Ree, R., The characters of G(q), Symposia Mathematica XIII, London 1974, pp. 395–4413. Google Scholar

[3] 3. Conder, M., A family of Hurwitz groups with non-trivial centres, Bull. Austr. Math. Soc. 33 (1986), pp. 123–130. Google Scholar

[4] 4. Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A., Wilson, R. A., Atlas of finite groups, Clarendon Press 1985, Oxford. Google Scholar

[5] 5. Cooperstein, B. N., Maximal subgroups of G(2n), J. Algebra 70 (1981), pp. 23–36. Google Scholar

[6] 6. Enomoto, H., The conjugacy classes of Chevalley groups of type (G) over finite fields of characteristic 2 or 3, J. Fac. Sci. Univ. Tokyo 16 (1970), pp. 497–512. Google Scholar

[7] 7. Enomoto, H., The characters of the finite Chevalley groups G(q), q = 3f, Japan J. Math. N.S. 2 (1976), pp. 191–248. Google Scholar

[8] 8. Kleidman, P., The maximal subgroups of the Chevalley groups G(q) with q odd, the Ree groups G(q) and of their automorphism groups, J. Algebra 117 (1988), pp. 30–71. Google Scholar

[9] 9. Macbeath, A. M., Generators of the linear fractional groups, Proc. Symp. Pure Math. 12 (1969), pp. 14–32. Google Scholar

[10] 10. Malle, G., Exceptional groups of Lie type as Galois groups, J. reine angew. Math. 392 (1988), pp. 70–109. Google Scholar

[11] 11. Matzat, B. H., Konstruktive Galoistheorie, Springer Lecture Notes 1284, Berlin - Heidelberg - New York 1987. Google Scholar

[12] 12. Simpson, W., Frame, J., The character tables for SL(q\ SU(q), PSL(q), U(q), Can. J. Math. 25 (1973), pp. 486–494. Google Scholar

[13] 13. Ward, H. N., On Ree's series of simple groups, Trans. Am. Math. Soc. 121 (1966), pp. 62–89. Google Scholar

Cité par Sources :