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arXiv · 1203.2728

On the maximal number of coprime subdegrees in finite primitive permutation groups

Silvio Dolfi·Robert Guralnick·Cheryl Praeger·Pablo Spiga
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Abstract

The subdegrees of a transitive permutation group are the orbit lengths of a point stabilizer. For a finite primitive permutation group which is not cyclic of prime order, the largest subdegree shares a non-trivial common factor with each non-trivial subdegree. On the other hand it is possible for non-trivial subdegrees of primitive groups to be coprime, a famous example being the rank 5 action of the small Janko group on 266 points which has subdegrees of lengths 11 and 12. We prove that, for every finite primitive group, the maximal size of a set of pairwise coprime non-trivial subdegrees is at most 2.

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Silvio Dolfi, Robert Guralnick, Cheryl Praeger, Pablo Spiga. 2012-03-13. On the maximal number of coprime subdegrees in finite primitive permutation groups. https://arxiv.org/abs/1203.2728

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