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On Soluble Groups of Automorphism of Riemann Surfaces

Published online by Cambridge University Press:  20 November 2018

Grzegorz Gromadzki
Grzegorz Gromadzki*
Affiliation:
Instytut Matematyki WSP Chodkiewicza 30 85-064 Bydgoszcz Poland and Universidad a Distancia Depto de Matem. Fund. 28040 Madrid Spain
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Abstract

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Let G be a soluble group of derived length 3. We show in this paper that if G acts as an automorphism group on a compact Riemann surface of genus g ≠ 3,5,6,10 then it has at most 24(g — 1) elements. Moreover, given a positive integer n we show the existence of a Riemann surface of genus g = n4 + 1 that admits such a group of automorphisms of order 24(g — 1), whilst a surface of specified genus can admit such a group of automorphisms of order 48(g — 1), 40(g — 1), 30(g — 1) and 36(g — 1) respectively.

Keywords

30F9920H1020D45
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 1 , 01 March 1991 , pp. 67 - 73
Copyright
Copyright © Canadian Mathematical Society 1991

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