Packing cycles in undirected group-labelled graphs

We prove a refinement of the flat wall theorem Robertson and Seymour to undirected group-labelled graphs (G,γ) where γ assigns each edge an graph G element abelian group Γ. As consequence, we that Γ-nonzero cycles (cycles whose labels sum non-identity Γ) satisfy half-integral Erdős-Pósa property, also recover result Wollan if Γ has no order two, then property. another application, m is odd prime power, length ℓmodm property for all integers ℓ. This partially answers question Dejter Neumann-Lara from 1987 on characterizing such integer pairs (ℓ,m).