Israel Journal of Mathematics

, Volume 21, Issue 1, pp 50–53 | Cite as

A note on transitive permutation groups of prime degree

  • David Chillag


LetG be a nonsolvable transitive permutation group of prime degreep. LetP be a Sylow-p-subgroup ofG and letq be a generator of the subgroup ofN G(P) fixing one point. Assume that |N G(P)|=p(p−1) and that there exists an elementj inG such thatj −1qj=q(p+1)/2. We shall prove that a group that satisfies the above condition must be the symmetric group onp points, andp is of the form 4n+1.


Symmetric Group Permutation Group Riemann Hypothesis Transitive Group Require Element 
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Copyright information

© The Weizmann Science Press of Israel 1975

Authors and Affiliations

  • David Chillag
    • 1
  1. 1.Department of MathematicsUniversity of IllinoisUrbanaU.S.A.

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