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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

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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

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