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The Conjecture is still open. Lemma 5 of math.GM/0204209 is false. For example, any primitive group on a prime number of points is a counterexampleto Lemma 5. Lemma 6 of math/0506617 is also false. Any transitive permutation group without a derangement of prime order satisfies the hypotheses and does not contain a semiregular element. (Any semiregular element has a power that is stil semiregular and of prime order.) Such groups exist, such as $M_{11}$ acting on the twelve points. |
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The Conjecture is still open. Lemma 5 of math.GM/0204209 is false. For example, any primitive group on a prime number of points is a counterexample to Lemma 5. Lemma 6 of math/0506617 is also false. Any transitive permutation group without a derangement of prime order satisfies the hypotheses and does not contain a semiregular element. (Any semiregular element has a power that is stil semiregular and of prime order.) Such groups exist, such as $M_{11}$ acting on the twelve points. |
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