## 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).…