Book contents
- Frontmatter
- Contents
- Contents of Volume 2
- Introduction
- Permutability and subnormality in finite groups
- (Pro)-finite and (topologically) locally finite groups with a CC-subgroup
- Table algebras generated by elements of small degrees
- Subgroups which are a union of a given number of conjugacy classes
- Some results on finite factorized groups
- On nilpotent-like Fitting formations
- Locally finite groups with min-p for all primes p
- Quasi-permutation representations of 2-groups of class 2 with cyclic centre
- Groups acting on bordered Klein surfaces with maximal symmetry
- Breaking points in subgroup lattices
- Group actions on graphs, maps and surfaces with maximum symmetry
- On dual pronormal subgroups and Fitting classes
- (p, q, r)-generations of the sporadic group O'N
- Computations with almost-crystallographic groups
- Random walks on groups: characters and geometry
- On distances of 2-groups and 3-groups
- Zeta functions of groups: the quest for order versus the flight from ennui
- Some factorizations involving hypercentrally embedded subgroups in finite soluble groups
- Elementary theory of groups
- Andrews-Curtis and Todd-Coxeter proof words
- Short balanced presentations of perfect groups
- Finite p-extensions of free pro-p groups
- Elements and groups of finite length
- Logged rewriting and identities among relators
- A characterization of F4(q) where q is an odd prime power
- On associated groups of rings
Groups acting on bordered Klein surfaces with maximal symmetry
Published online by Cambridge University Press: 11 January 2010
- Frontmatter
- Contents
- Contents of Volume 2
- Introduction
- Permutability and subnormality in finite groups
- (Pro)-finite and (topologically) locally finite groups with a CC-subgroup
- Table algebras generated by elements of small degrees
- Subgroups which are a union of a given number of conjugacy classes
- Some results on finite factorized groups
- On nilpotent-like Fitting formations
- Locally finite groups with min-p for all primes p
- Quasi-permutation representations of 2-groups of class 2 with cyclic centre
- Groups acting on bordered Klein surfaces with maximal symmetry
- Breaking points in subgroup lattices
- Group actions on graphs, maps and surfaces with maximum symmetry
- On dual pronormal subgroups and Fitting classes
- (p, q, r)-generations of the sporadic group O'N
- Computations with almost-crystallographic groups
- Random walks on groups: characters and geometry
- On distances of 2-groups and 3-groups
- Zeta functions of groups: the quest for order versus the flight from ennui
- Some factorizations involving hypercentrally embedded subgroups in finite soluble groups
- Elementary theory of groups
- Andrews-Curtis and Todd-Coxeter proof words
- Short balanced presentations of perfect groups
- Finite p-extensions of free pro-p groups
- Elements and groups of finite length
- Logged rewriting and identities among relators
- A characterization of F4(q) where q is an odd prime power
- On associated groups of rings
Summary
Abstract
A finite group G is said to be an M*-group if it is the group of automorphisms of a bordered compact Klein surface with maximal symmetry. M*-groups play an analogous role for Klein surfaces as Hurwitz groups do for Riemann surfaces. In this survey we present a summary of results on M*-groups. We first examine their properties and the known families of M*-groups. Then we study their structure to obtain new methods for constructing additional families. Finally we examine the relationship between Hurwitz groups, H*-groups and M*-groups.
Introduction
The study of Riemann and Klein surfaces with maximal automorphism groups has a long history. It is well known that a compact Riemann surface of genus g ≥ 2 admits at most 84(g – 1) automorphisms. Automorphism groups of Riemann surfaces with this maximal number of automorphisms are called Hurwitz groups. It is known that Hurwitz groups exist for infinitely many values of g and also do not exist for infinitely many g. The article by Conder [9] contains a nice survey of known results about Hurwitz groups. Corresponding problems concerning Klein surfaces have also received a good deal of attention and we present a summary of known results here.
A Klein surface is the orbit space of a Riemann surface under the action of a symmetry, that is, an anticonformal automorphism of order two. The algebraic genus of the Klein surface is defined to be the genus of its Riemann double cover.
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- Groups St Andrews 2001 in Oxford , pp. 50 - 58Publisher: Cambridge University PressPrint publication year: 2003
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