scholarly journals On automorphism groups of circulant digraphs of square-free order

2005 ◽  
Vol 299 (1-3) ◽  
pp. 79-98 ◽  
Author(s):  
Edward Dobson ◽  
Joy Morris
Keyword(s):  
Automorphism Groups ◽  
Free Order ◽  
Circulant Digraphs

scholarly journals On Edge-Transitive Graphs of Square-Free Order

10.37236/4573 ◽  
2015 ◽  
Vol 22 (3) ◽  
Author(s):  
Cai Heng Li ◽  
Zai Ping Lu ◽  
Gai Xia Wang
Keyword(s):  
Automorphism Groups ◽  
Edge Transitive ◽  
Transitive Graphs ◽  
Free Order

We study the class of  edge-transitive graphs of square-free order and valency at most $k$. It is shown that, except for a few special families of graphs, only finitely many members in this class are basic (namely, not a normal multicover of another member). Using this result, we determine the automorphism groups of locally primitive arc-transitive graphs with square-free order.

scholarly journals The Automorphism Groups of Minimal Infinite Circulant Digraphs

1997 ◽  
Vol 18 (4) ◽  
pp. 425-429 ◽  
Author(s):  
Jixiang Meng ◽  
Huang Qiongxing
Keyword(s):  
Automorphism Groups ◽  
Circulant Digraphs

AUTOMORPHISM GROUPS OF SELF-COMPLEMENTARY VERTEX-TRANSITIVE GRAPHS

2015 ◽  
Vol 93 (2) ◽  
pp. 238-247
Author(s):  
ZHAOHONG HUANG ◽  
JIANGMIN PAN ◽  
SUYUN DING ◽  
ZHE LIU
Keyword(s):  
Automorphism Group ◽  
Simple Group ◽  
Automorphism Groups ◽  
Composition Factor ◽  
Vertex Transitive ◽  
Vertex Transitive Graphs ◽  
Transitive Graphs ◽  
Free Order

Li et al. [‘On finite self-complementary metacirculants’, J. Algebraic Combin.40 (2014), 1135–1144] proved that the automorphism group of a self-complementary metacirculant is either soluble or has $\text{A}_{5}$ as the only insoluble composition factor, and gave a construction of such graphs with insoluble automorphism groups (which are the first examples of self-complementary graphs with this property). In this paper, we will prove that each simple group is a subgroup (so is a section) of the automorphism groups of infinitely many self-complementary vertex-transitive graphs. The proof involves a construction of such graphs. We will also determine all simple sections of the automorphism groups of self-complementary vertex-transitive graphs of $4$-power-free order.

scholarly journals Automorphism Groups of Circulant Digraphs With Applications to Semigroup Theory

COMBINATORICA ◽  
2017 ◽  
Vol 38 (1) ◽  
pp. 1-28 ◽  
Author(s):  
João Araújo ◽  
Wolfram Bentz ◽  
Edward Dobson ◽  
Janusz Konieczny ◽  
Joy Morris
Keyword(s):  
Automorphism Groups ◽  
Semigroup Theory ◽  
Circulant Digraphs

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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