scholarly journals Highly transitive actions of groups acting on trees

2015 ◽  
Vol 143 (12) ◽  
pp. 5083-5095 ◽  
Author(s):  
Pierre Fima ◽  
Soyoung Moon ◽  
Yves Stalder
Keyword(s):  
Groups Acting On Trees ◽  
Transitive Actions

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.

scholarly journals Bridging Semisymmetric and Half-Arc-Transitive Actions on Graphs

2002 ◽  
Vol 23 (6) ◽  
pp. 719-732 ◽  
Author(s):  
Dragan Marušič ◽  
Primož Potočnik
Keyword(s):  
Transitive Actions

scholarly journals Maximal Subgroups and Irreducible Representations of Generalized Multi-Edge Spinal Groups

2018 ◽  
Vol 61 (3) ◽  
pp. 673-703 ◽  
Author(s):  
Benjamin Klopsch ◽  
Anitha Thillaisundaram
Keyword(s):  
Rooted Tree ◽  
Maximal Subgroups ◽  
Irreducible Representations ◽  
Prime Field ◽  
Infinite Dimensional ◽  
Special Cases ◽  
Profinite Completions ◽  
Spinal Group ◽  
Groups Acting On Trees ◽  
Image Position

AbstractLet p ≥ 3 be a prime. A generalized multi-edge spinal group $$G = \langle \{ a\} \cup \{ b_i^{(j)} {\rm \mid }1 \le j \le p,\, 1 \le i \le r_j\} \rangle \le {\rm Aut}(T)$$ is a subgroup of the automorphism group of a regular p-adic rooted tree T that is generated by one rooted automorphism a and p families $b^{(j)}_{1}, \ldots, b^{(j)}_{r_{j}}$ of directed automorphisms, each family sharing a common directed path disjoint from the paths of the other families. This notion generalizes the concepts of multi-edge spinal groups, including the widely studied GGS groups (named after Grigorchuk, Gupta and Sidki), and extended Gupta–Sidki groups that were introduced by Pervova [‘Profinite completions of some groups acting on trees, J. Algebra310 (2007), 858–879’]. Extending techniques that were developed in these more special cases, we prove: generalized multi-edge spinal groups that are torsion have no maximal subgroups of infinite index. Furthermore, we use tree enveloping algebras, which were introduced by Sidki [‘A primitive ring associated to a Burnside 3-group, J. London Math. Soc.55 (1997), 55–64’] and Bartholdi [‘Branch rings, thinned rings, tree enveloping rings, Israel J. Math.154 (2006), 93–139’], to show that certain generalized multi-edge spinal groups admit faithful infinite-dimensional irreducible representations over the prime field ℤ/pℤ.

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