I'm currently reading about the Krull-Schmidt Theorem for groups, and am wondering how I can learn more about its role in group theory. Thus far I have read the proof sketch given in Hungerford's algebra and done the exercises in the chapter pertaining to K-S, but there are only two of them, and I am looking to see what types of broader insights this theorem might offer about groups.
The KS theorem for groups seems incredibly powerful, but whenever I attempt to research it I find the KS theorem for rings and modules or Krull-Schmidt Categories.
I did end up reading about formulating Krull-Schmidt using projective covers, but lack an intuition for what this would look like in the category of groups with the bi-chain condition.
Does anyone have suggestions for papers or other references?