Derangements and p-elements in permutation groups
نویسنده
چکیده
2. (Jordan) A transitive permutation group of degree n > 1 contains a derangement. In fact (Cameron and Cohen) the proportion of derangements in a transitive group G is at least 1/n. Equality holds if and only if G is sharply 2transitive, and hence is the affine group {x 7→ ax + b : a, b ∈ F, a 6= 0} over a nearfield F. The finite nearfields were determined by Zassenhaus. They all have prime power order.
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