caa a22 4500 38637211X CHVBK 20180307112001.0 cr unu---uuuuu 161130e198909 xx s 000 0 eng 10.1017/S0017089500007886 doi S0017089500007886 pii (NATIONALLICENCE)cambridge-10.1017/S0017089500007886 Supersoluble groups of automorphisms of compact Riemann surfaces [Elektronische Daten] 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: Copyright © Glasgow Mathematical Journal Trust 1989 Gromadzki Grzegorz Instytut Matematyki WSP, Chodkiewicza 30, 85-064 Bydgoszcz, Poland. and, Universidad a Distancia, Depto de Matem, Fund. 28040 Madrid, Spain. MacLachlan Colin Department of Mathematics, University of Aberdeen, The Edward Wright Building, Dunbar Street, Aberdeen AB9 2TY Glasgow Mathematical Journal Cambridge University Press 31/3(1989-09), 321-327 0017-0895 31:3<321 1989 31 GMJ https://doi.org/10.1017/S0017089500007886 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0017089500007886 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Gromadzki Grzegorz Instytut Matematyki WSP, Chodkiewicza 30, 85-064 Bydgoszcz, Poland. and, Universidad a Distancia, Depto de Matem, Fund. 28040 Madrid, Spain NATIONALLICENCE 700 1- MacLachlan Colin Department of Mathematics, University of Aberdeen, The Edward Wright Building, Dunbar Street, Aberdeen AB9 2TY NATIONALLICENCE 773 0- Glasgow Mathematical Journal Cambridge University Press 31/3(1989-09), 321-327 0017-0895 31:3<321 1989 31 GMJ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence SWISSBIB 38637211X BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge