  In this paper, we introduce a weakening of the Freiman isomorphisms between
subsets of non necessarily abelian groups.
  Inspired by the breakthrough result of Kravitz, [14], on cyclic groups, as a
first application, we prove that any subset of size $k$ of the dihedral group
$D_{2m}$ (and, more in general, of a class of semidirect products) is
sequenceable, provided that the prime factors of $m$ are larger than $k!$.
Also, a refined bound of $k!/2$ for the size of the prime factors of $m$ can be
obtained for cyclic groups $\mathbb{Z}_m$, slightly improving the result of
[14]. Then, applying again the concept of weak Freiman isomorphism, we show
that any subset of size $k$ of the dicyclic group $\mathrm{Dic}_{m}$ is
sequenceable, provided that the prime factors of $m$ are larger than $k^k$.
