A note on transitive permutation groups of prime degree
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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.
KeywordsSymmetric Group Permutation Group Riemann Hypothesis Transitive Group Require Element
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