11.36 (1990)

Let $G = B(m, n)$ be the free Burnside group of rank $m$ and of odd exponent $n \gg 1$. Are the following statements true?
$\qquad$ a) Every 2-generated subgroup of $G$ is isomorphic to the Burnside $n$-product of two cyclic groups.
$\qquad$ b) Every automorphism $\varphi$ of $G$ such that $\varphi^n = 1$ and $b^\varphi \cdot b^{\varphi^2} \cdots b^{\varphi^n} = 1$ for all $b \in G$ is an inner automorphism (here $m > 1$).
$\qquad$ c) The group $G$ is Hopfian if $m < \infty$.
$\qquad$ d) All retracts of $G$ are free.
$\qquad$ e) Is it true that all zero divisors in the group ring $\mathbb{Z}G$ are trivial? which means that if $ab = 0$ then $a = a_1 c$, $b = db_1$ where $a_1, c, b_1, d \in \mathbb{Z}G$, $cd = 0$, and the set $\text{supp}\,c \cup \text{supp}\,d$ is contained in a cyclic subgroup of $G$.