Geodesic
Fully invariant subgroups of an infinitely iterated wreath product
Algebra and discrete mathematics, Tome 12 (2011) no. 2, pp. 85-93

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The article deals with the infinitely iterated wreath product of cyclic groups $C_p$ of prime order $p$. We consider a generalized infinite wreath product as a direct limit of a sequence of finite $n$th wreath powers of $C_p$ with certain embeddings and use its tableau representation. The main result are the statements that this group doesn't contain a nontrivial proper fully invariant subgroups and doesn't satisfy the normalizer condition.
Keywords: wreath product, fully invariant subgroups. 
@article{ADM_2011_12_2_a7,
     author = {Yuriy Yu. Leshchenko},
     title = {Fully invariant subgroups of an infinitely iterated wreath product},
     journal = {Algebra and discrete mathematics},
     pages = {85--93},
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     volume = {12},
     number = {2},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2011_12_2_a7/}
}
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Yuriy Yu. Leshchenko. Fully invariant subgroups of an infinitely iterated wreath product. Algebra and discrete mathematics, Tome 12 (2011) no. 2, pp. 85-93. http://geodesic.mathdoc.fr/item/ADM_2011_12_2_a7/