### Impacto

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

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

## 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 |
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Uncontrolled Keywords: | Automorphisms; Riemann surfaces; Weierstrass points; gap sequences |

Subjects: | Sciences > Mathematics > Algebraic geometry |

ID Code: | 15788 |

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Deposited On: | 27 Jun 2012 11:44 |

Last Modified: | 06 Feb 2014 10:31 |

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