Flag-Transitive Point-Primitive Automorphism Groups of Nonsymmetric 2−(v,k,2) Designs

2016 ◽  
Vol 24 (9) ◽  
pp. 421-435 ◽  
Author(s):  
Hongxue Liang ◽  
Shenglin Zhou
Keyword(s):  
Automorphism Groups ◽  
Transitive Point

Line-transitive point-imprimitive linear spaces with number of points being a product of two primes

2017 ◽  
Vol 16 (06) ◽  
pp. 1750110
Author(s):  
Haiyan Guan ◽  
Shenglin Zhou
Keyword(s):  
Linear Space ◽  
Automorphism Groups ◽  
Linear Spaces ◽  
Finite Linear Space ◽  
Transitive Point ◽  
Finite Linear

The work studies the line-transitive point-imprimitive automorphism groups of finite linear spaces, and is underway on the situation when the numbers of points are products of two primes. Let [Formula: see text] be a non-trivial finite linear space with [Formula: see text] points, where [Formula: see text] and [Formula: see text] are two primes. We prove that if [Formula: see text] is line-transitive point-imprimitive, then [Formula: see text] is solvable.

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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