60 citations · 145 across the 38 of their papers we have counts for
21 papers · 1 filter
Hole operations on Hurwitz maps
Gábor Gévay, Gareth A. Jones
For a given group the orientably regular maps with orientation-preserving automorphism group are used as the vertices of a graph , with undirected and directed edges…
Finite simple automorphism groups of edge-transitive maps
Gareth A. Jones
Building on earlier results for regular maps and for orientably regular chiral maps, we classify the non-abelian finite simple groups arising as automorphism groups of maps in each…
Groups of prime degree and the Bateman-Horn Conjecture
Gareth A. Jones, Alexander K. Zvonkin
As a consequence of the classification of finite simple groups, the classification of permutation groups of prime degree is complete, apart from the question of when the natural de…
Klein's ten planar dessins of degree 11, and beyond
Gareth A. Jones, Alexander K. Zvonkin
We reinterpret ideas in Klein's paper on transformations of degree from the modern point of view of dessins d'enfants, and extend his results by considering dessins of type $(…
A short proof of Greenberg's Theorem
Gareth A. Jones
Greenberg proved that every countable group is isomorphic to the automorphism group of a Riemann surface, which can be taken to be compact if is finite. We give a short and…
Joining dessins together
Gareth A. Jones
An operation of joining coset diagrams for a given group, introduced by Higman and developed by Conder in connection with Hurwitz groups, is reinterpreted and generalised as a conn…
Realisation of groups as automorphism groups in categories
Gareth A. Jones
It is shown that in various categories, including many consisting of maps or hypermaps, oriented or unoriented, of a given hyperbolic type, every countable group is isomorphic…
Maximal subgroups of the modular and other groups
Gareth A. Jones
In 1933 B.~H.~Neumann constructed uncountably many subgroups of which act regularly on the primitive elements of . As pointed out by Magnus, th…
Automorphism groups of maps, hypermaps and dessins
Gareth A. Jones
A detailed proof is given of a theorem describing the centraliser of a transitive permutation group, with applications to automorphism groups of objects in various categories of ma…
Doubly Hurwitz Beauville groups
Gareth A. Jones, Emilio Pierro
If is a Beauville surface , then the Hurwitz bound implies that , with equality if and only if th…
The Möbius Function of the Suzuki Groups
Martin Downs, Gareth A. Jones
We compute the Möbius function for the subgroup lattice of the simple Suzuki group ; this is used to enumerate normal subgroups of certain Hecke groups with quotients isomor…
Regular dessins with a given automorphism group
Gareth A. Jones
Dessins d'enfants are combinatorial structures on compact Riemann surfaces defined over algebraic number fields, and regular dessins are the most symmetric of them. If G is a finit…
Enumerating Regular Objects associated with Suzuki Groups
Martin Downs, Gareth A. Jones
We use the Möbius function of the simple Suzuki group Sz(q) to enumerate regular objects such as maps, hypermaps, dessins d'enfants and surface coverings with automorphism groups i…
Characteristically simple Beauville groups, II: low rank and sporadic groups
Gareth A. Jones
A Beauville surface is a rigid complex surface of general type, isogenous to a higher product by the free action of a finite group, called a Beauville group. Here we consider which…
Characteristically simple Beauville groups, I: cartesian powers of alternating groups
Gareth A. Jones
A Beauville surface (of unmixed type) is a complex algebraic surface which is the quotient of the product of two curves of genus at least 2 by a finite group G acting freely on the…
Primitive permutation groups containing a cycle
Gareth A. Jones
The primitive finite permutation groups containing a cycle are classified. Of these, only the alternating and symmetric groups contain a cycle fixing at least three points. The con…
2-Groups that factorise as products of cyclic groups, and regular embeddings of complete bipartite graphs
Shaofei Du, Gareth Jones, Jin Ho Kwak +2
We classify those 2-groups G which factorise as a product of two disjoint cyclic subgroups A and B, transposed by an automorphism of order 2. The case where G is metacyclic having…
Hyperbolic manifolds and tessellations of type {3,5,3} associated with L_2(q)
Gareth A. Jones, Cormac D. Long, Alexander D. Mednykh
We classify the normal subgroups K of the tetrahedral group Delta=[3,5,3]^+, the even subgroup of the Coxeter group Gamma=[3,5,3], with Delta/K isomorphic to a finite simple group…
Automorphism groups of Beauville surfaces
Gareth A. Jones
This paper shows that the automorphism group of a Beauville surface is a finite solvable group, and describes its possible structure. It relies on results of Singerman on triangle…
Beauville surfaces and finite groups
Yolanda Fuertes, Gareth Jones
Extending results of Bauer, Catanese and Grunewald, and of Fuertes and González-Diez, we show that Beauville surfaces of unmixed type can be obtained from the groups L_2(q) and SL_…
A bound for the number of automorphisms of an arithmetic Riemann surface
M. Belolipetsky, G. A. Jones
We show that for every g > 1 there is a compact arithmetic Riemann surface of genus g with at least 4(g-1) automorphisms, and that this lower bound is attained by infinitely many g…