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.

MSC: 20B22, 20E18, 20E22

Received: 15.04.2011
Revised: 19.12.2011

Language: English

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