scholarly journals Automorphism Groups of Cayley Maps

1993 ◽  
Vol 59 (2) ◽  
pp. 297-310 ◽  
Author(s):  
R. Jajcay
Keyword(s):  
Automorphism Groups ◽  
Cayley Maps

scholarly journals Automorphism groups of Cayley graphs generated by block transpositions and regular Cayley maps

2017 ◽  
Vol 340 (1) ◽  
pp. 3125-3139 ◽  
Author(s):  
Annachiara Korchmaros ◽  
István Kovács
Keyword(s):  
Automorphism Groups ◽  
Cayley Graphs ◽  
Cayley Maps

Cayley maps and symmetrical maps

1972 ◽  
Vol 72 (3) ◽  
pp. 381-386 ◽  
Author(s):  
Norman Biggs
Keyword(s):  
Complete Graph ◽  
Automorphism Groups ◽  
Main Concern ◽  
Classical Theorem ◽  
Trivial Vertex ◽  
Vertex Transitive ◽  
Special Case ◽  
Orientable Surfaces ◽  
Combinatorial Methods ◽  
Cayley Maps

AbstractIn this paper we shall show how combinatorial methods can be applied to the study of maps on orientable surfaces. Our main concern is with maps which possess a certain kind of symmetry, called vertex-transitivity. We show how an extension of the well-known method of Cayley can be used to construct such maps, and we give conditions which suffice for the automorphism groups of these maps to have non trivial vertex-stabilizers. Finally, we investigate the special case when the skeleton of the map is a complete graph; a classical theorem of Frobenius then implies that all vertex-transitive maps are given by our extension of Cayley's construction.

Pentavalent 1-Transitive Digraphs with Non-Solvable Automorphism Groups

2020 ◽  
Vol 51 (4) ◽  
pp. 1919-1930
Author(s):  
Masoumeh Akbarizadeh ◽  
Mehdi Alaeiyan ◽  
Raffaele Scapellato
Keyword(s):  
Automorphism Groups

Regular Cayley maps for dihedral groups

2021 ◽  
Vol 148 ◽  
pp. 84-124
Author(s):  
István Kovács ◽  
Young Soo Kwon
Keyword(s):  
Dihedral Groups ◽  
Cayley Maps

scholarly journals Serre’s Property (FA) for automorphism groups of free products

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Naomi Andrew
Keyword(s):  
Automorphism Group ◽  
Free Product ◽  
Finite Groups ◽  
Automorphism Groups ◽  
Sufficient Conditions ◽  
Free Products ◽  
Cyclic Groups ◽  
Link Type ◽  
Open Case

AbstractWe provide some necessary and some sufficient conditions for the automorphism group of a free product of (freely indecomposable, not infinite cyclic) groups to have Property (FA). The additional sufficient conditions are all met by finite groups, and so this case is fully characterised. Therefore, this paper generalises the work of N. Leder [Serre’s Property FA for automorphism groups of free products, preprint (2018), https://arxiv.org/abs/1810.06287v1]. for finite cyclic groups, as well as resolving the open case of that paper.

scholarly journals Geometrically rational real conic bundles and very transitive actions

2010 ◽  
Vol 147 (1) ◽  
pp. 161-187 ◽  
Author(s):  
Jérémy Blanc ◽  
Frédéric Mangolte
Keyword(s):  
Automorphism Groups ◽  
Algebraic Surfaces ◽  
Algebraic Models ◽  
Transitive Automorphism ◽  
Real Locus ◽  
Real Algebraic Surfaces ◽  
Conic Bundles ◽  
Transitive Actions ◽  
Insight Into

AbstractIn this article we study the transitivity of the group of automorphisms of real algebraic surfaces. We characterize real algebraic surfaces with very transitive automorphism groups. We give applications to the classification of real algebraic models of compact surfaces: these applications yield new insight into the geometry of the real locus, proving several surprising facts on this geometry. This geometry can be thought of as a half-way point between the biregular and birational geometries.

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