Symmetries in graphs, maps, and polytopes : 5th SIGMAP Workshop, West Malvern, UK, July 2014 /: 5th SIGMAP Workshop, West Malvern, UK, July 2014. ([2016])

• Record Type: Book
• Other Titles: SIGMAP Workshop
• Further Information: Note: Jozef Širáň, Robert Jajcay, editors.
• Editors: Širáň, Jozef; Jajcay, Robert
• Other Names: Symmetries In Graphs, Mans, And Polytopes Workshop, 5th
• Contents: Preface; Acknowledgements; Contents; Powers of Skew-Morphisms; 1 Introduction; 2 Basic Properties of Skew-Morphisms and Their Relation to Cayley Maps; 3 Generalization of t-Balanced Skew-Morphisms; 4 Powers of Skew-Morphisms; 5 Coset-Preserving Powers; 6 Coset-Preserving Skew-Morphisms of Cyclic Groups; References; Census of Quadrangle Groups Inclusions; 1 Introduction; 2 Generalised Quadrangle Groups and Constellations; 3 How to Read the Census; References; Some Unexpected Consequences of Symmetry Computations; 1 Introduction; 2 Arc-Transitive Cubic Graphs and SL(3, mathbbZ) 3 Sierpinski's Gasket and Binary Gray Codes4 Regular Maps; References; A 3D Spinorial View of 4D Exceptional Phenomena; 1 Introduction; 2 Root Systems and Reflection Groups; 3 Clifford Versor Framework; 4 H4 as a Rotation Rather Than Reflection Group I: From E8; 5 H4 as a Rotation Rather Than Reflection Group II: From H3; 6 The General Construction: Spinor Induction and the 4D Platonic Solids, Trinities and McKay Correspondence; 7 Group and Representation Theory with Clifford Multivectors; 8 Conclusion; References; Möbius Inversion in Suzuki Groups and Enumeration of Regular Objects. 1 Introduction2 Categories and Groups; 2.1 Maps, Hypermaps and Groups; 2.2 Reflexibility; 2.3 Covering Spaces; 3 Counting Homomorphisms; 4 The Suzuki Groups and Their Subgroups; 4.1 The Definition of the Suzuki Groups; 4.2 Basic Properties of Suzuki Groups; 4.3 Some Particular Subgroups; 4.4 The Möbius Function of a Suzuki Group; 5 Subgroups H with G (H); 5.1 Maxint Subgroups; 5.2 Maximal Subgroups; 5.3 Point-Stabilisers in Maximal Subgroups; 5.4 Subgroups H of F; 5.5 Subgroups H of Bi; 6 Size of Conjugacy Classes; 7 Calculating Values of muG; 8 Enumerations; 8.1 Orientably Regular Hypermaps. 8.2 Regular Hypermaps8.3 Orientably Regular Maps; 8.4 Regular Maps; 8.5 Surface Coverings; 9 The Smallest Simple Suzuki Group; 10 Postscript; References; More on Strongly Real Beauville Groups; 1 Introduction; 2 Preliminaries; 3 The Finite Simple Groups; 4 Characteristically Simple Groups; 5 Almost Simple Groups; 6 The Groups G:langlegrangletimesG:langlegrangle; 7 Abelian and Nilpotent Groups; References; On Pentagonal Geometries with Block Size 3, 4 or 5; 1 Introduction; 2 Constructions; 3 Block Size 3; 4 Block Sizes 4 and 5; 5 The Case r=2k+1; 6 Concluding Remarks; References. The Grothendieck-Teichmüller Group of a Finite Group and G-Dessins d'enfants1 Introduction; 2 Generalities; 2.1 The Group gb; 2.2 The Group gts(G); 2.3 Inverse Limits; 2.4 The Galois Group of mathbbQ; 2.5 p-Groups and Nilpotent Groups; 3 An Elementary Example: Dihedral Groups; 4 The Case of Simple Groups; 4.1 Notation; 4.2 An Action of outgb on pc; 4.3 The Group mathscrS(G); 4.4 Properties of mathscrS(G); 4.5 A Complete Example; 5 Computing Explicitly; 5.1 Computing gts1G; 5.2 Computing sG; 5.3 Simple Groups of Small Order; 5.4 p-Groups; 6 Dessins d'enfants; 6.1 The Category of Dessins.
• Publisher Details: Switzerland : Springer
• Publication Date: 2016
• Copyright Date: 2016
• Extent: 1 online resource, illustrations
• Subjects: 516.1; Mathematics; Symmetry (Mathematics) -- Congresses; Mathematics -- Graphic methods -- Congresses; MATHEMATICS / Geometry / General; Mathematics -- Graphic methods; Symmetry (Mathematics); Mathematics -- Algebra -- Abstract; Mathematics -- Group Theory; Algebra; Groups & group theory; Field theory (Physics); Topological Groups; Mathematics -- Graphic Methods; Combinatorics & graph theory; Electronic books; Conference papers and proceedings
• Languages: English
• ISBNs: 9783319304519; 3319304518
• Related ISBNs: 9783319304496; 3319304496
• Notes: Note: Includes bibliographical references.; Note: Online resource; title from PDF title page (Ebsco, viewed March 30, 2016).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.