Cyclic Renormalization and Automorphism Groups of Rooted Trees

1996 ◽  
Author(s):  
Hyman Bass ◽  
Maria Victoria Otero-Espinar ◽  
Daniel Rockmore ◽  
Charles Tresser
Keyword(s):  
Automorphism Groups ◽  
Rooted Trees

Automorphism groups of rooted trees have property (FA): A new proof

2012 ◽  
Vol 15 (2) ◽  
Author(s):  
Maciej Malicki
Keyword(s):  
Automorphism Groups ◽  
Rooted Trees

Abstract.We give a new proof of a theorem of Psaltis

scholarly journals On an Identity for the Cycle Indices of Rooted Tree Automorphism Groups

10.37236/1152 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
Stephan G. Wagner
Keyword(s):  
Symmetric Group ◽  
Elementary Proof ◽  
Automorphism Groups ◽  
Rooted Tree ◽  
Rooted Trees ◽  
Cycle Index ◽  
Spanning Forest ◽  
Cycle Indices

This note deals with a formula due to G. Labelle for the summed cycle indices of all rooted trees, which resembles the well-known formula for the cycle index of the symmetric group in some way. An elementary proof is provided as well as some immediate corollaries and applications, in particular a new application to the enumeration of $k$-decomposable trees. A tree is called $k$-decomposable in this context if it has a spanning forest whose components are all of size $k$.

CONJUGATION IN TREE AUTOMORPHISM GROUPS

2001 ◽  
Vol 11 (05) ◽  
pp. 529-547 ◽  
Author(s):  
PIOTR W. GAWRON ◽  
VOLODYMYR V. NEKRASHEVYCH ◽  
VITALY I. SUSHCHANSKY
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Rooted Tree ◽  
Symmetric Groups ◽  
Wreath Products ◽  
Rooted Trees ◽  
Full Description ◽  
Finite Tree ◽  
Locally Finite ◽  
Infinite Sequences

It is given a full description of conjugacy classes in the automorphism group of the locally finite tree and of a rooted tree. They are characterized by their types (a labeled rooted trees) similar to the cyclical types of permutations. We discuss separately the case of a level homogenous tree, i.e. conjugality in wreath products of infinite sequences of symmetric groups. It is proved those automorphism groups of rooted and homogenous non-rooted trees are ambivalent.

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

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.

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