Generation of iterated wreath products constructed from alternating, symmetric and cyclic groups

Jiaping Lu; Martyn Quick

paper

Generation of iterated wreath products constructed from alternating, symmetric and cyclic groups

arXiv:2501.17524

Abstract

Let $G_{1}$ , $G_{2}$ , ... be a sequence of groups each of which is either an alternating group, a symmetric group or a cyclic group and construct a sequence $(W_{i})$ of wreath products via $W_{1} = G_{1}$ and, for each $i \geq 1$ , $W_{i + 1} = G_{i + 1} wr G_{i}$ via the natural permutation action. We determine the minimum number $d (W_{i})$ of generators required for each wreath product in this sequence.

16 pages, 1 figure. To appear in Internat. J. Algebra Comput