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A subset A $A$ of an abelian group G $G$ is sequenceable if there is an ordering (a1,...,ak) $({a}_{1},\ldots ,{a}_{k})$ of its elements such that the partial sums (s0,s1,...,sk) $({s}_{0},{s}_{1},\ldots ,{s}_{k})$, given by s0=0 ${s}_{0}=0$ and si=∑j=1iaj ${s}_{i}={\sum }_{j=1}^{i}{a}_{j}$ for 1≤i≤k $1\le i\le k$, are distinct, with the possible exception that we may have sk=s0=0 ${s}_{k}={s}_{0}=0$. In the literature there are several conjectures and questions concerning the sequenceability of subsets of abelian groups, which have been combined and summarized by Alspach and Liversidge into the conjecture that if a subset of an abelian group does not contain 0 then it is sequenceable. If the elements of a sequenceable set A $A$ do not sum to 0 then there exists a simple path P $P$ in the Cayley graph Cay[G:±A] $Cay[G:\pm A]$ such that Δ(P)=±A ${\rm{\Delta }}(P)=\pm A$. In this paper, inspired by this graph–theoretical interpretation, we propose a weakening of this conjecture. Here, under the above assumptions, we want to find an ordering whose partial sums define a walk W $W$ of girth bigger than t $t$ (for a given t