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

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 J 1 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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Correspondence to Silvio Dolfi.

Additional information

Address correspondence to P. Spiga, e-mail: pablo.spiga@unimib.it

The first author is partially supported by GNSAGA.

The second author was partially supported by the NSF grant DMS-1302886 and the Simons Foundation Fellowship 224965.

The third author was supported by the ARC Federation Fellowship Project FF0776186.

The fourth author was supported by the University of Western Australia as part of the Federation Fellowship project.

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Dolfi, S., Guralnick, R., Praeger, C.E. et al. On the maximal number of coprime subdegrees in finite primitive permutation groups. Isr. J. Math. 216, 107–147 (2016). https://doi.org/10.1007/s11856-016-1405-7

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  • DOI: https://doi.org/10.1007/s11856-016-1405-7