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Supersoluble groups of automorphisms of compact Riemann surfaces

Published online by Cambridge University Press:  18 May 2009

Grzegorz Gromadzki  and
Colin MacLachlan
Grzegorz Gromadzki
Affiliation:
Instytut Matematyki WSP, Chodkiewicza 30, 85–064 Bydgoszcz, Poland. and, Universidad a Distancia, Depto de Matem, Fund. 28040 Madrid, Spain.
Colin MacLachlan
Affiliation:
Department of Mathematics, University of Aberdeen, The Edward Wright Building, Dunbar Street, Aberdeen AB9 2TY
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Given an integer g ≥ 2 and a class of finite groups let N(g, ) denote the order of the largest group in that a compact Riemann surface of genus g admits as a group of automorphisms. For the classes of all finite groups, cyclic groups, abelian groups, nilpotent groups, p-groups (given p), soluble groups and finally for metabelian groups, an upper bound for N(g, ) as well as infinite sequences for g for which this bound is attained were found in [5, 6, 7, 8, 13], [4], [10], [15], [16], [1], [2] respectively. This paper deals with that problem for the class of finite supersoluble groups i.e. groups with an invariant series all of whose factors are cyclic. In addition, it goes further by describing exactly those values of g for which the bound is attained. More precisely we prove:

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 31 , Issue 3 , September 1989 , pp. 321 - 327
Copyright
Copyright © Glasgow Mathematical Journal Trust 1989

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