Geodesic
Wreath products and periodic factorable groups
Sbornik. Mathematics, Tome 67 (1990) no. 2, pp. 535-553 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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[5] Suschanskii V. I., “Spleteniya po posledovatelnostyam grupp podstanovok i finitno approksimiruemye gruppy”, DAN USSR. Ser. A, 1984, no. 2, 19–22 | Zbl

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[7] Kaluzhnin L. A., Suschanskii V. I., “O spleteniyakh abelevykh grupp”, Tr. MMO, 29, 1973, 147–163 | Zbl

[8] Suschanskii V. I., “Predstavlenie finitno approksimiruemykh $p$-grupp izometriyami prostranstva tselykh $p$-adicheskikh chisel”, DAN USSR. Ser. A, 1986, no. 5, 23–26 | Zbl

[9] Suschanskii V. Ya., “Periodicheskie $p$-gruppy podstanovok i neogranichennaya problema Bernsaida”, DAN SSSR, 247:3 (1979), 557–561 | MR | Zbl

[10] Grigorchuk R. I., “K probleme Bernsaida o periodicheskikh gruppakh”, Funktsion. analiz i ego pril., 14:1 (1980), 53–54 | MR | Zbl