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Archiv der Mathematik

, Volume 72, Issue 6, pp 405–417 | Cite as

On minimal p-degrees in 2-transitive permutation groups

  • Jens Höchsmann
Article

Abstract.

Suppose G is a transitive permutation group on a finite set \(\mit\Omega \) of n points and let p be a prime divisor of \(|G|\). The smallest number of points moved by a non-identity p-element is called the minimal p-degree of G and is denoted mp (G). ¶ In the article the minimal p-degrees of various 2-transitive permutation groups are calculated. Using the classification of finite 2-transitive permutation groups these results yield the main theorem, that \(m_{p}(G) \geq {{p-1} \over {p+1}} \cdot |\mit\Omega |\) holds, if \({\rm Alt}(\mit\Omega ) \nleqq G \).¶Also all groups G (and prime divisors p of \(|G|\)) for which \(m_{p}(G)\le {{p-1}\over{p}} \cdot |\mit\Omega |\) are identified.

Keywords

Permutation Group Prime Divisor 

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Copyright information

© Birkhäuser Verlag, Basel 1999

Authors and Affiliations

  • Jens Höchsmann
    • 1
  1. 1.Guttenbrunnweg 3, D-89165 DietenheimDeutschland

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