Finitely generated groups without the minimal condition on subgroups

Question

Definition

A group $G$ is said to satisfies the minimal condition on subgroups iff every descending chain of subgroups stops after a finite number of steps.

I know Novikon and Adjan proved that the Burnside group $F/F^m$ (where $F$ is a free group of finite rank $n>0$ and $m$ is an odd integer grower than $4381$) is infinite and satisfies the minimal condition on abelian subgroups. Obviously it is countable.

Question: Does the Burnside group $F/F^m$ satisfies the minimal condition on subgroups?

I think the question can be reformulated in the following way:

Is there a finitely generated group $G$ with finite odd exponent such that $G$ do not satisfies to minimal condition on subgroups?

Answer 1

The wreath product of two Tarski monsters. (I think.)