Iterated wreath products generated by alternating, symmetric and cyclic groups

设 $G_{1}$, $G_{2}$, ... 为一序列群,每个群均为交错群、对称群或循环群.通过 $W_{1} = G_{1}$ 及对每个 $i \geq 1$, $W_{i+1} = G_{i+1} \operatorname{wr} G_{i}$ (由自然置换作用)构造一序列 $(W_{i})$ 的包庄积.我们确定每个包庄积在该序列中所需的生成器最小数目 $d(W_{i})$。