scholarly journals Metacyclic groups of automorphisms of compact Riemann surfaces

2001 ◽  
Vol 31 (1) ◽  
pp. 117-132 ◽  
Author(s):  
A. A. George Michael
Keyword(s):  
Riemann Surfaces ◽  
Metacyclic Groups ◽  
Groups Of Automorphisms ◽  
Compact Riemann Surfaces

Dihedral Groups of Automorphisms of Compact Riemann Surfaces

1998 ◽  
Vol 41 (2) ◽  
pp. 252-256 ◽  
Author(s):  
Qingjie Yang
Keyword(s):  
Riemann Surfaces ◽  
Group Actions ◽  
Dihedral Groups ◽  
Groups Of Automorphisms ◽  
Compact Riemann Surfaces

AbstractIn this note we determine which dihedral subgroups of GLg(ℂ) can be realized by group actions on Riemann surfaces of genus g > 1.

scholarly journals On symmetries of compact Riemann surfaces with cyclic groups of automorphisms

2006 ◽  
Vol 301 (1) ◽  
pp. 82-95 ◽  
Author(s):  
E. Bujalance ◽  
F.J. Cirre ◽  
J.M. Gamboa ◽  
G. Gromadzki
Keyword(s):  
Riemann Surfaces ◽  
Cyclic Groups ◽  
Groups Of Automorphisms ◽  
Compact Riemann Surfaces

scholarly journals Supersoluble groups of automorphisms of compact Riemann surfaces

1989 ◽  
Vol 31 (3) ◽  
pp. 321-327 ◽  
Author(s):  
Grzegorz Gromadzki ◽  
Colin MacLachlan
Keyword(s):  
Finite Groups ◽  
Riemann Surfaces ◽  
Nilpotent Groups ◽  
Metabelian Groups ◽  
Supersoluble Groups ◽  
Soluble Groups ◽  
Cyclic Groups ◽  
Groups Of Automorphisms ◽  
Compact Riemann Surfaces ◽  
Infinite Sequences

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:

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