It would be best to use the default setting of the group set which is Pass Through and to apply the mode changes on the layer rather than the Set. In this way, if you add more layers with different modes, Pass Through will blend any layer within the group as if there's no grouping,
I can't explain it in technical terms but changing the Set's mode to anything else will have a different, unexpected effect. It will blend the layers within the group first and the result is again blended with the layers below and outside the group using the blend mode selected for the group. Thus if you have say several layers in the group and set at different modes, the layer settings are cancelled out and will be blended in the mode that is set for that group.
So use Pass through - the Group set's default setting.
edit..... ohh Goooood lord.... less than 60 seconds apart with MrTom...... :banghead: :hi:
edit02...... I forgot to mention.... the effect you're getting with the group blend mode set to Linear Dodge with normal layer mode content is like painting the stripe directly on the base image (layer 1) with a brush set to Linear Dodge.