158 Citations
Finite simple groups acting with fixity 3 and their occurrence as groups of automorphisms of Riemann surfaces
- MathematicsCommunications in Algebra
- 2021
Abstract The results in this article are based on the classification of finite simple groups that act with fixity 3. Motivated by the theory of Riemann surfaces, we investigate which ones of these…
A note on minimal finite quotients of mapping class groups
- Mathematics
- 2008
We prove that the minimal nontrivial finite quotient group of the mapping class group M_g of a closed orientable surface of genus g is the symplectic group PSp(2g,Z_2), for g = 3 and 4 (this might…
A lower bound for the number of group actions on a compact Riemann surface
- Mathematics
- 2012
We prove that the number of distinct group actions on compact Riemann surfaces of a fixed genus g (at least 2) is at least quadratic in g. We do this through the introduction of a coarse signature…
Generation of finite subgroups of the mapping class group of genus 2 surface by Dehn twists
- MathematicsJournal of Pure and Applied Algebra
- 2018
The occurrence of finite simple permutation groups of fixity 2 as automorphism groups of Riemann surfaces
- Mathematics
- 2020
On Cyclic Groups of Automorphisms of Riemann Surfaces
- Mathematics
- 1999
The question of extendability of the action of a cyclic group of automorphisms of a compact Riemann surface is considered. Particular attention is paid to those cases corresponding to Singerman's…
The genus level of a group
- Mathematics
- 2009
We introduce the notion of the genus level of a group as a tool to help classify finite conformal group actions on compact Riemann surfaces. We classify all groups of genus level 1 and use our…
Finite abelian subgroups of the mapping class group
- Mathematics
- 2007
The problem of enumeration of conjugacy classes of finite abelian sub- groups of the mapping class group Mof a compact closed surface X of genusis considered. A complete method of enumeration is…
References
SHOWING 1-10 OF 91 REFERENCES
Finite Groups of Mapping Classes of Surfaces
- Mathematics
- 1981
On the Nielsen realization problem, preliminaries.- Tori, crystallographic groups and the realization of mapping classes.- Marked Riemann surfaces and Fuchsian groups and Fenchel's realization…
A simple presentation for the mapping class group of an orientable surface
- Mathematics
- 1983
LetFn.k be an orientable compact surface of genusn withk boundary components. For a suitable choice of 2n + 1 simple closed curves onFn,1 the corresponding Dehn twists generate bothMn,o andMn,1. A…
Finite groups acting on surfaces and the genus of a group
- MathematicsJ. Comb. Theory, Ser. B
- 1983
On branch loci in Teichmüller space
- Mathematics
- 1971
The branch locus of the ramified covering of the space of moduli of Fuchsian groups with fixed presentation by the corresponding Teichmiller space is decomposed into a union of Teichmiuller spaces,…
Some results on quotients of triangle groups
- MathematicsBulletin of the Australian Mathematical Society
- 1984
Given positive integers k, l, m, the (k, l, m) triangle group has presentation δ(k, l, m) = < X, Y, Z | Xk = Yl = Zm = XYZ = 1 >. This paper considers finite permutation representations of such…
Torsion free subgroups of Fuchsian groups and tessellations of surfaces
- Mathematics
- 1982
It has been known for many years that a finitely generated fuchsian group G i.e. a finitely generated discrete subgroup of orientation-preserving isometries of the hyperbolic plane contains a torsion…
Groups related to compact Riemann surfaces
- Mathematics
- 1969
I t has been known for a long time tha t the automorphism group of a compact Riemann surface of genus g > 1 is a finite group. Indeed, Hurwitz gave the upper bound of 8 4 ( g 1) for the order. In…
The non-abelian simple groups g, |g| < 106— character tables
- Mathematics
- 1979
Character tables are presented for all the 56 non-abelian simple groups of order up to 106, including three tables for the family PSL(2,q) and twenty tables for individual groups (with some overlap).…