Geodesic
Wreath products and periodic factorable groups
Sbornik. Mathematics, Tome 67 (1990) no. 2, pp. 535-553

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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. 
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     author = {V. I. Sushchanskii},
     title = {Wreath products and periodic factorable groups},
     journal = {Sbornik. Mathematics},
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     number = {2},
     year = {1990},
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     url = {http://geodesic.mathdoc.fr/item/SM_1990_67_2_a11/}
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V. I. Sushchanskii. Wreath products and periodic factorable groups. Sbornik. Mathematics, Tome 67 (1990) no. 2, pp. 535-553. http://geodesic.mathdoc.fr/item/SM_1990_67_2_a11/