Generation of iterated wreath products constructed from almost simple groups

Abstract Let G 1 G_{1} , G 2 G_{2} , … be a sequence of almost simple groups and construct a sequence ( W i ) (W_{i}) of wreath products via W 1 = G 1 W_{1}=G_{1} and, for each i > 1 i>1 , W i + 1 = G i + 1 wr W i W_{i+1}=G_{i+1}\mathbin{\mathrm{wr}}W_{i} via the regular action of each G i G_{i} . We determine the minimum number d ⁢ ( W i ) d(W_{i}) of generators required for each wreath product in this sequence.