AbstractA subset of an abelian group is sequenceable if there is an ordering of its elements such that the partial sums , given by and for , are distinct, with the possible exception that we may have . 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 do not sum to 0 then there exists a simple path in the Cayley graph such that . 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 of girth bigger than (for a given ) and such that . This is possible given that the partial sums and are different whenever and are distinct and . In this case, we say that the set is ‐weakly sequenceable. The main result here presented is that any subset of is ‐weakly sequenceable whenever or when does not contain pairs of type and .