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 J1 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.
On the maximal number of coprime subdegrees in finite primitive permutation groups / Dolfi, Silvio; Guralnick, Robert; Praeger, Cheryl E.; Spiga, Pablo. - In: ISRAEL JOURNAL OF MATHEMATICS. - ISSN 0021-2172. - STAMPA. - 216:(2016), pp. 107-147. [10.1007/s11856-016-1405-7]
On the maximal number of coprime subdegrees in finite primitive permutation groups
DOLFI, SILVIO;
2016
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 J1 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.File | Dimensione | Formato | |
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OnTheMaximalNumberOfCoprimeSubdegrees.pdf
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