Some results on quotients of triangle groups
TLDR
In this article, the (k, l, m) triangle group has a presentation δ(k,l, m), where m is the number of vertices in the triangle group.Abstract:
Given positive integers k, l, m, the (k, l, m) triangle group has presentation δ(k, l, m) = . This paper considers finite permutation representations of such groups. In particular it contains descriptions of graphical and computational techniques for handling them, leading to new results on minimal two-element generation of the finite alternating and symmetric groups and the group of Rubik's cube. Applications to the theory of regular maps and automorphisms of surfaces are also discussed.read more
Citations
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Journal ArticleDOI
Classifying finite group actions on surfaces of low genus
TL;DR: In this article, the problem of classifying all finite group actions, up to topological equivalence, on a surface of low genus, is considered and several new examples of construction and classification of actions are given.
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The symmetric genus of sporadic groups
TL;DR: In this paper, the problem of determining the symmetric genus for sporadic simple groups was solved for all but nine groups: J3, McL, Suz, O'N, Q>2, Fi23, Co, Co,, B, and M.
Journal ArticleDOI
The symmetric genus of alternating and symmetric groups
TL;DR: The symmetric genus of a finite group G has been defined by Thomas W. Tucker as the smallest genus of all surfaces on which G acts faithfully as a group of automorphisms (some of which may reverse the orientation of the surface).
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References
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Book
Generators and relations for discrete groups
H. S. M. Coxeter,W. O. J. Moser +1 more
TL;DR: In this article, the authors present a systematic enumeration of cosets based on the following groups: cyclic, Dicyclic and Metacyclic groups, Graphs, Maps, Cayley Diagrams, Hyperbolic Tessellations and Fundamental Groups.
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Permutation Groups and Combinatorial Structures
Norman Biggs,Arthur T. White +1 more
TL;DR: In this paper, the action of permutation groups on sets associated with combinatorial structures is discussed, and a theory of maps on orientable surfaces is developed within a combinatorical framework.
Journal ArticleDOI
Subgroups of Fuchsian Groups and Finite Permutation Groups
TL;DR: In this article, the authors consider the problem of determining necessary and sufficient conditions for a subgroup of finite index in F to have some given signature, where the generators are the elements which map the region onto a full neighbour.