Fully invariant subgroups of an infinitely iterated wreath product

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.