On the automorphisms of 2−(v,k,1) designs

Shangzhao Li, Weijun Liu and Xianhua Li

Applied Mathematics and Computation, 2017, vol. 292, issue C, 120-127

Abstract: Thirty years ago, a six-person team classified the pairs (D,G) where D is a 2−(v,k,1) design and G is a flag-transitive automorphism group of D, with the exception of those in which G is a one-dimensional affine group. Since then the effort has been to classify those D, designs which are block-transitive but not flag-transitive. This paper contributes to the program for determining the pairs 2−(v,k,1) in which (D,G) has a block-transitive group G of automorphisms. It is clear that if one wishes to study the structure of a finite group acting on a D design then describing the socle is an important first step. Here we prove that if G is a block-transitive group of automorphisms of 2−(v,k,1) which has D as its socle then T is also transitive on the blocks of T=2F4(q).

Keywords: Block-transitive; D design; Automorphism; Socle (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:292:y:2017:i:c:p:120-127

DOI: 10.1016/j.amc.2016.06.027

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