Block-transitive automorphism groups on 3-designs with small block size
Xiaoqin Zhan, Meifang Yang

TL;DR
This paper classifies the structure of block-transitive automorphism groups of small block size 3-designs, showing they are either affine or almost simple if point-primitive, and describing specific cases if point-imprimitive.
Contribution
It provides a classification of automorphism groups for 3-designs with block size up to 6, distinguishing between primitive and imprimitive cases and detailing their structures.
Findings
Point-primitive groups are of affine or almost simple type.
Point-imprimitive groups correspond to a specific 3-(16,6,λ) design with known λ values.
The rank of such groups is always 3.
Abstract
The paper is an investigation of the structure of block-transitive automorphism groups of a 3-design with small block size. Let be a block-transitive automorphism group of a nontrivial - design with . We prove that if is point-primitive then is of affine or almost simple type. If is point-imprimitive then is a - design with , and .
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Taxonomy
TopicsFinite Group Theory Research · Coding theory and cryptography · graph theory and CDMA systems
