Wreath products and periodic factorable groups

Wreath products of sequences of permutation groups are applied to construct groups decomposable as products of permuting subgroups. A natural factorization is exhibited for such wreath products, corresponding to direct decompositions of the wreathed groups and a partitioning of the index set into nonintersecting subsets. A general construction for producing factorable subgroups of wreath products is described here. It is used to make an example of a residually finite periodic but not locally finite group decomposable as a product of locally finite subgroups; this answers a question of V. P. Shunkov in the negative.
Bibliography: 10 titles.