10.1 (1986)

Let $p$ be a prime number. Describe the groups of order $p^9$ of nilpotency class 2 which contain subgroups $X$ and $Y$ such that $|X| = |Y| = p^3$ and any non-identity elements $x \in X$, $y \in Y$ do not commute. An answer to this question would yield a description of the semifields of order $p^3$.