Fully invariant subgroups of an infinitely iterated wreath product

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.