Primitive permutation groups whose subdegrees are bounded above

2012/01/04 by Simon M. Smith, Smith, Simon M.
Computer Science · Mathematics · #20B07 #20B10 #20B15 #Advanced Algebra and Geometry #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #math.GR #msc:20B07 #msc:20B10 #msc:20B15

paper · pdf · doi:10.48550/arxiv.1201.0803

Comments welcome

arxiv created 2012/01/04 · openalex publication_date 2012/01/04 · arxiv updated 2012/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

If G is a group of permutations of a set Ω and α∈ Ω, then the \em α-suborbits of G are the orbits of the stabilizer G_α on Ω. The cardinality of an α-suborbit is called a \em subdegree of G. If the only G-invariant equivalence classes on Ω are the trivial and universal relations, then G is said to be a \em primitive group of permutations of Ω. In this paper we determine the structure of all primitive permutation groups whose subdegrees are bounded above by a finite cardinal number.

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