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 Algebra Discrete Math.: Year: Volume: Issue: Page: Find

 Algebra Discrete Math., 2011, Volume 12, Issue 2, Pages 85–93 (Mi adm132)

RESEARCH ARTICLE

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

Abstract: 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.

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Bibliographic databases:
MSC: 20B22, 20E18, 20E22
Revised: 19.12.2011
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Citation: Yuriy Yu. Leshchenko, “Fully invariant subgroups of an infinitely iterated wreath product”, Algebra Discrete Math., 12:2 (2011), 85–93

Citation in format AMSBIB
\Bibitem{Les11} \by Yuriy Yu. Leshchenko \paper Fully invariant subgroups of an infinitely iterated wreath product \jour Algebra Discrete Math. \yr 2011 \vol 12 \issue 2 \pages 85--93 \mathnet{http://mi.mathnet.ru/adm132} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2952904} \zmath{https://zbmath.org/?q=an:1257.20035}