scholarly journals Hausdorff dimension of the second Grigorchuk group

2021 ◽  
pp. 1-11
Author(s):  
Marialaura Noce ◽  
Anitha Thillaisundaram
Keyword(s):  
Automorphism Group ◽  
Hausdorff Dimension ◽  
Full Automorphism Group ◽  
Grigorchuk Group

We show that the Hausdorff dimension of the closure of the second Grigorchuk group is 43/128. Furthermore, we establish that the second Grigorchuk group is super strongly fractal and that its automorphism group equals its normalizer in the full automorphism group of the tree.

scholarly journals Cohomological finiteness conditions and centralisers in generalisations of Thompson’s group V

2016 ◽  
Vol 28 (5) ◽  
pp. 909-921 ◽  
Author(s):  
Conchita Martínez-Pérez ◽  
Francesco Matucci ◽  
Brita E. A. Nucinkis
Keyword(s):  
Automorphism Group ◽  
Finiteness Conditions ◽  
Group V ◽  
Full Automorphism Group ◽  
Finite Subgroups ◽  
Thompson’S Group

AbstractWe consider generalisations of Thompson’s group V, denoted by ${V_{r}(\Sigma)}$, which also include the groups of Higman, Stein and Brin. We show that, under some mild hypotheses, ${V_{r}(\Sigma)}$ is the full automorphism group of a Cantor algebra. Under some further minor restrictions, we prove that these groups are of type ${\operatorname{F}_{\infty}}$ and that this implies that also centralisers of finite subgroups are of type ${\operatorname{F}_{\infty}}$.

scholarly journals Pentavalent arc-transitive Cayley graphs on Frobenius groups with soluble vertex stabilizer

2019 ◽  
Vol 17 (1) ◽  
pp. 513-518
Author(s):  
Hailin Liu
Keyword(s):  
Automorphism Group ◽  
Cayley Graph ◽  
Cayley Graphs ◽  
Frobenius Groups ◽  
Full Automorphism Group

Abstract A Cayley graph Γ is said to be arc-transitive if its full automorphism group AutΓ is transitive on the arc set of Γ. In this paper we give a characterization of pentavalent arc-transitive Cayley graphs on a class of Frobenius groups with soluble vertex stabilizer.

scholarly journals Rooted trees, strong cofinality and ample generics

2012 ◽  
Vol 154 (2) ◽  
pp. 213-223
Author(s):  
MACIEJ MALICKI
Keyword(s):  
Automorphism Group ◽  
Open Subgroup ◽  
Rooted Trees ◽  
Full Automorphism Group

AbstractWe characterize those countable rooted trees with non-trivial components whose full automorphism group has uncountable strong cofinality, and those whose full automorphism group contains an open subgroup with ample generics.

A 2-ARC TRANSITIVE PENTAVALENT CAYLEY GRAPH OF 

2016 ◽  
Vol 93 (3) ◽  
pp. 441-446 ◽  
Author(s):  
BO LING ◽  
BEN GONG LOU
Keyword(s):  
Automorphism Group ◽  
Cayley Graph ◽  
Cayley Graphs ◽  
Discrete Math ◽  
Simple Groups ◽  
Alternating Group ◽  
Full Automorphism Group ◽  
Symmetric Graphs

Zhou and Feng [‘On symmetric graphs of valency five’, Discrete Math. 310 (2010), 1725–1732] proved that all connected pentavalent 1-transitive Cayley graphs of finite nonabelian simple groups are normal. We construct an example of a nonnormal 2-arc transitive pentavalent symmetric Cayley graph on the alternating group $\text{A}_{39}$. Furthermore, we show that the full automorphism group of this graph is isomorphic to the alternating group $\text{A}_{40}$.

Full automorphism group of the generalized symplectic graph

2013 ◽  
Vol 56 (7) ◽  
pp. 1509-1520 ◽  
Author(s):  
LiWei Zeng ◽  
Zhao Chai ◽  
RongQuan Feng ◽  
ChangLi Ma
Keyword(s):  
Automorphism Group ◽  
Full Automorphism Group

scholarly journals The automorphism group of the -orbifold of the Barnes–Wall lattice vertex operator algebra of central charge 32

2014 ◽  
Vol 156 (2) ◽  
pp. 343-361 ◽  
Author(s):  
HIROKI SHIMAKURA
Keyword(s):  
Automorphism Group ◽  
Vertex Operator ◽  
Operator Algebra ◽  
Vertex Operator Algebra ◽  
Central Charge ◽  
Group Structure ◽  
Graph Structure ◽  
Full Automorphism Group ◽  
Lattice Vertex Operator Algebra

AbstractIn this paper, we prove that the full automorphism group of the ${\mathbb Z}_2$-orbifold of the Barnes–Wall lattice vertex operator algebra of central charge 32 has the shape 227.E6(2). In order to identify the group structure, we introduce a graph structure on the Griess algebra and show that it is a rank 3 graph associated to E6(2).

scholarly journals A 2-arc Transitive Hexavalent Nonnormal Cayley Graph on A119

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2935
Author(s):  
Bo Ling ◽  
Wanting Li ◽  
Bengong Lou
Keyword(s):  
Automorphism Group ◽  
Cayley Graph ◽  
Automorphism Groups ◽  
Cayley Graphs ◽  
Vital Role ◽  
Alternating Group ◽  
Full Automorphism Group ◽  
Base Group

A Cayley graph Γ=Cay(G,S) is said to be normal if the base group G is normal in AutΓ. The concept of the normality of Cayley graphs was first proposed by M.Y. Xu in 1998 and it plays a vital role in determining the full automorphism groups of Cayley graphs. In this paper, we construct an example of a 2-arc transitive hexavalent nonnormal Cayley graph on the alternating group A119. Furthermore, we determine the full automorphism group of this graph and show that it is isomorphic to A120.

scholarly journals A New Near Octagon and the Suzuki Tower

10.37236/5067 ◽  
2016 ◽  
Vol 23 (2) ◽  
Author(s):  
Anurag Bishnoi ◽  
Bart De Bruyn
Keyword(s):  
Automorphism Group ◽  
Strongly Regular Graphs ◽  
Regular Graphs ◽  
Geometric Constructions ◽  
Full Automorphism Group ◽  
Strongly Regular

We construct and study a new near octagon of order $(2,10)$ which has its full automorphism group isomorphic to the group $G_2(4):2$ and which contains $416$ copies of the Hall-Janko near octagon as full subgeometries. Using this near octagon and its substructures we give geometric constructions of the $G_2(4)$-graph and the Suzuki graph, both of which are strongly regular graphs contained in the Suzuki tower. As a subgeometry of this octagon we have discovered another new near octagon, whose order is $(2,4)$.

Sign in / Sign up

Export Citation Format

Share Document