Complutense University Library

Alternating groups, Hurwitz groups and H*-groups

Etayo Gordejuela, J. Javier and Martínez García, Ernesto (2005) Alternating groups, Hurwitz groups and H*-groups. Journal of Algebra, 283 (1). pp. 327-349. ISSN 0021-8693

[img] PDF
Restricted to Repository staff only until 31 December 2020.

165kB

Official URL: http://www.sciencedirect.com/science/article/pii/S0021869304004259

View download statistics for this eprint

==>>> Export to other formats

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.

Item Type:Article
Uncontrolled Keywords:Automorphisms; Riemann surfaces; Weierstrass points; gap sequences
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:15788
References:

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.

Deposited On:27 Jun 2012 11:44
Last Modified:06 Feb 2014 10:31

Repository Staff Only: item control page