  Let $k=\mathbb{Q}_3(\theta)$, $\theta^3=1$ be a quadratic extension of 3-adic
numbers. Let $V$ be a cubic surface defined over a field $k$ by the equation
$T_0^3+T_1^3+T_2^3+\theta T_0^3=0$ and let $V(k)$ be a set of rational points
on $V$ defined over $k$. We show that a relation on $V(k)$ modulo a prime
$(1-\theta)^3$ (in a ring of integers of $k$) defines an admissible relation on
a set of rational points of $V$ over $k$ and a commutative Moufang loop
associated with classes of this admissible equivalence on $V(k)$ is
non-associative. This answers a long standing problem that was formulated by
Yu. I. Manin more than 50 years ago about existence of non-abelian quasi-groups
associated with some cubic surface over some field.
