A finite transitive permutation group is said to be elusive if it has no fixed-point free elements of prime order. In this paper we show that all elusive groups G N x G(1) with N an elementary abelian minimal normal subgroup and G(1) cyclic, can be constructed from transitive subgroups of AGL(1, p(2)), for p a Mersenne prime, acting on the set of p(p + 1) lines of the affine plane AG(2, p).
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机译：如果有限的传递置换群没有素数阶的定点自由元素，则它是难以捉摸的。在本文中，我们表明，对于pa Mersenne，可以从AGL（1，p（2））的传递子组构造所有具有N个基本阿贝尔最小正态子组和G（1）循环的GN x G（1）的难以捉摸的组素数，作用在仿射平面AG（2，p）的p（p + 1）条线上。
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