A Theorem of Siemons and Wagner

2018/08/31 by Paul Bradley, Bradley, Paul
Computer Science · Engineering · Mathematics · #20B20 20B15 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1808.10832

openalex publication_date 2018/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 1988 Siemons and Wagner describe a relationship between the lengths of G-orbits on subsets of a G-set Ω. They highlighted the situation where Δ⊂ Ω with |Δ|=k, and |Δ^G|>|Σ^G| for all (k+1)-subsets, Σ of Ω where Δ⊂Σ. They went on to classify all primitive groups with this property for k=2. Here we address some questions about primitive permutation groups satisfying this property when k=3 and list all 3-homogeneous groups satisfying this condition.

Citations

• Finite Permutation Groups and Finite Simple Groups

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