Publication: Alternating groups, Hurwitz groups and H*-groups
Loading...
Full text at PDC
Publication Date
2005
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Academic Press
Citations
Exportar
Abstract
The authors obtain the pairs of generators, necessary to study the non-orientable case, of the alternating groups $A_n$ for $n=15$, 21, 22, 28 and 29, which are also Hurwitz groups, groups with maximal number of automorphisms on Riemann surfaces. The results found here can be applied to handle the corresponding problem on non-orientable surfaces. In particular, they show that the ones for $n=15$ and 28 match the bound for non-orientable surfaces, while the ones for $n=21$, 22 and 29 do not. They also obtain some other Hurwitz groups which are at the same time proper subgroups of the alternating groups. They obtain a way of deciding which alternating groups are also $H^*$-groups.
Description
UCM subjects
Unesco subjects
Keywords
Citation
N.L. Alling, N. Greenleaf, Foundations of the theory of Klein surfaces, Lecture Notes in Math., vol. 219, Springer-Verlag, New York, 1971.
M.D.E. Conder, Generators for alternating and symmetric groups, J. London Math. Soc. (2) 22 (1980) 75–86.
M.D.E. Conder, Some results on quotients of triangle groups, Bull. Austral. Math. Soc. 29 (1984) 73–90.
M.D.E. Conder, Groups of minimal genus including C2 extensions of PSL(2,q) for certain q, Quart. J. Math. Oxford (2) 38 (1987) 449–460.
M.D.E. Conder, Hurwitz groups: a brief survey, Bull. Amer. Math. Soc. 23 (1990) 359–370.
H.M.S. Coxeter, The abstract groups Gm,n,p, Trans. Amer. Math. Soc. 45 (1939) 73–150.
A.M. Macbeath, The classification of non-Euclidean crystallographic groups, Canad. J. Math. 6 (1967) 1192–1205.
C.L. May, Large automorphism groups of compact Klein surfaces with boundary, Glasgow Math. J. 18 (1977) 1–10.
R. Preston, Projective structures and fundamental domains on compact Klein surfaces, Thesis, Univ. of Texas, 1975.
D. Singerman, Automorphisms of compact non-orientable Riemann surfaces, Glasgow Math. J. 12 (1971) 50–59.
D. Singerman, On the structure of non-Euclidean crystallographic groups, Proc. Cambridge Philos. Soc. 76 (1974) 233–240.
H.C. Wilkie, On non-Euclidean crystallographic groups, Math. Z. 91 (1966) 87–102.