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
10.37236/4573 ◽  
2015 ◽  
Vol 22 (3) ◽  
Author(s):  
Cai Heng Li ◽  
Zai Ping Lu ◽  
Gai Xia Wang

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.


1997 ◽  
Vol 18 (4) ◽  
pp. 425-429 ◽  
Author(s):  
Jixiang Meng ◽  
Huang Qiongxing

2015 ◽  
Vol 93 (2) ◽  
pp. 238-247
Author(s):  
ZHAOHONG HUANG ◽  
JIANGMIN PAN ◽  
SUYUN DING ◽  
ZHE LIU

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.


COMBINATORICA ◽  
2017 ◽  
Vol 38 (1) ◽  
pp. 1-28 ◽  
Author(s):  
João Araújo ◽  
Wolfram Bentz ◽  
Edward Dobson ◽  
Janusz Konieczny ◽  
Joy Morris

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

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Naomi Andrew

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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