For a permutation group G on a set S, the movement of G is defined as the maximum cardinality of subsets T of S for which there exists an element x is an element of G such that T is disjoint from its translate TX (that is, when such subsets have bounded cardinality). It was shown by the second author that, if G has bounded movement m and if G has no fixed points in S, then S is finite, and ISI is bounded above by a function of m. In particular, if G is transitive, then S less than or equal to 3m. This paper completes the proof of a conjecture of Gardiner and Praeger that the only transitive groups on a set of size 3m which have movement m are transitive permutation groups of exponent 3 (when m is a power of 3), the symmetric group S-3 in its natural representation on a set of three points, and the alternating groups A(4) and A(5), in their transitive representations on six points. (C) 1996 Academic Press, Inc. [References: 15]
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机译：对于集合S上的置换组G，G的运动定义为S的子集T的最大基数，对于该子集T，存在一个元素x是G的元素，使得T与它的平移TX不相交（即，当此类子集具有受限基数时）。第二作者表明，如果G限制了运动m，并且G在S中没有固定点，则S是有限的，并且ISI在上方被m函数限制。特别是，如果G是可传递的，则 S 小于或等于3m。本文完成了对Gardiner和Praeger猜想的证明：在大小为3m的集合上，唯一具有运动m的传递组是指数3的传递置换组（当m为3的幂时），对称组S-3在三个点的集合上以自然表示形式出现，在六个点的传递表示中以交替组A（4）和A（5）出现。 （C）1996 Academic Press，Inc. [参考：15]
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