Fully invariant subgroups of an infinitely iterated wreath product
Yuriy Yu. Leshchenko
Department of Algebra and Mathematical Analysis, Bogdan Khmelnitsky National University, 81, Shevchenko blvd., Cherkasy, 18031, Ukraine
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.
wreath product, fully invariant subgroups.
PDF file (239 kB)
MSC: 20B22, 20E18, 20E22
Yuriy Yu. Leshchenko, “Fully invariant subgroups of an infinitely iterated wreath product”, Algebra Discrete Math., 12:2 (2011), 85–93
Citation in format AMSBIB
\by Yuriy Yu. Leshchenko
\paper Fully invariant subgroups of an infinitely iterated wreath product
\jour Algebra Discrete Math.
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