Auslander-Reiten quivers of group rings

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Let RG be an integral group ring of a finite group G over a complete discrete valuation ring R with residue class field k of positive characteristic. Suppose that L is an indecomposable RG-lattice of height zero, and let S be a source of L. We have shown that the tree class of the Auslander-Reiten component containing L is A-infinity if and only if the tree class of the Auslander-Reiten component containing S is A-infinity. Also, we have proved that the middle term of the almost split sequence terminating in L is indecomposable if the reduced kG-module of L is indecomposable. In the case of 2-modular system, we have shown that the tree classes of the Auslander-Reiten components containing odd rank RG-lattices are A-infinity.