Classification of the non-trivial 2-$$(v,k,\lambda )$$ designs, with $$ (r,\lambda )=1$$ and $$\lambda >1$$, admitting a non-solvable flag-transitive automorphism group of affine type

2021 ◽  
Author(s):  
Alessandro Montinaro ◽  
Mauro Biliotti ◽  
Eliana Francot
Keyword(s):  
Automorphism Group ◽  
Transitive Automorphism ◽  
Transitive Automorphism Group ◽  
Affine Type

scholarly journals On transitive commutative idempotent quasigroups

1979 ◽  
Vol 27 (4) ◽  
pp. 411-429
Author(s):  
Arnold Neumaier
Keyword(s):  
Automorphism Group ◽  
Transitive Automorphism ◽  
Transitive Automorphism Group ◽  
Recursive Constructions ◽  
Room Squares ◽  
Sharply Transitive

AbstractCommutative idempotent quasigroups with a sharply transitive automorphism group G are described in terms of so-called Room maps of G. Orthogonal Room maps and skew Room maps are used to construct Room squares and skew Room squares. Very general direct and recursive constructions for skew Room maps lead to the existence of skew Room maps of groups of order prime to 30. Also some nonexistence results are proved.

Reduction for primitive flag-transitive nonsymmetric 2-(v,k,4) designs

2019 ◽  
Vol 19 (12) ◽  
pp. 2050240 ◽  
Author(s):  
Yongli Zhang ◽  
Zhilin Zhang ◽  
Shenglin Zhou
Keyword(s):  
Automorphism Group ◽  
Simple Type ◽  
Transitive Automorphism ◽  
Text Design ◽  
Transitive Automorphism Group

Let [Formula: see text] be a nonsymmetric 2-[Formula: see text] design and [Formula: see text] be a primitive flag-transitive automorphism group of [Formula: see text]. Then [Formula: see text] must be of affine or almost simple type.

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