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A Group Labeled Graph is a pair $(G,\Lambda)$ where $G$ is an oriented graphand $\Lambda$ is a mapping from the arcs of $G$ to elements of a group. A (notnecessarily directed) cycle $C$ is called non-null if for any cyclic orderingof the arcs in $C$, the group element obtained by `adding' the labels onforward arcs and `subtracting' the labels on reverse arcs is not the identityelement of the group. Non-null cycles in group labeled graphs generalizeseveral well-known graph structures, including odd cycles.  In this paper, we prove that non-null cycles on Group Labeled Graphs have thehalf-integral Erd\"os-P\'osa property. That is, there is a function $f:{\mathbbN}\to {\mathbb N}$ such that for any $k\in {\mathbb N}$, any group labeledgraph $(G,\Lambda)$ has a set of $k$ non-null cycles such that each vertex of$G$ appears in at most two of these cycles or there is a set of at most $f(k)$vertices that intersects every non-null cycle. Since it is known that non-nullcycles do not have the integeral Erd\"os-P\'osa property in general, ahalf-integral Erd\"os-P\'osa result is the best one could hope for.

The Half-integral Erd\"os-P\'osa Property for Non-null Cycles