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

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

2012-03-13

arxiv.org/abs/1203.2728v1

Mathematics

Group Theory

Scientific paper

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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