Finite generation of iterated wreath products in product action
Tóm tắt
Let
$${\mathcal{S}}$$
be a sequence of finite perfect transitive permutation groups with uniformly bounded number of generators. We prove that the infinitely iterated wreath product in product action of the groups in
$${\mathcal{S}}$$
is topologically finitely generated, provided that the actions of the groups in
$${\mathcal{S}}$$
are never regular. We also deduce that certain infinitely iterated wreath products obtained by a mixture of imprimitive and product actions of groups in
$${\mathcal{S}}$$
are finitely generated. Finally we apply our methods to find explicitly two generators of infinitely iterated wreath products in product action of certain sequences
$${\mathcal{S}}$$
of 2-generated perfect groups.
Từ khóa
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