Finite primitive groups and regular orbits of group elements

2014/06/06 by Simon Guest, Pablo Spiga, Guest, Simon +1
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #math.CO #math.GR

paper · pdf · doi:10.48550/arxiv.1406.1702

21 pages

arxiv created 2014/06/06 · arxiv updated 2014/06/09

Abstract

We prove that if G is a finite primitive permutation group and if g is an element of G, then either g has a cycle of length equal to its order, or for some r, m and k, the group G ≤ Sym(m) \textrmwr Sym(r) preserves the product structure of r direct copies of the natural action of Sym(m) on k-sets. This gives an answer to a question of Siemons and Zalesski and a solution to a conjecture of Giudici, Praeger and the second author.

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