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?

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    $\begingroup$ If i remember correctly the earliest time I read about it was during the development of composition series $\endgroup$ – Alexander Gruber Oct 12 '18 at 23:18
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    $\begingroup$ See also here; some people call it Remak-Krull-Schmidt, but this should be the same. It is more important for modules, see wikipedia. $\endgroup$ – Dietrich Burde Oct 13 '18 at 8:17
  • $\begingroup$ thank you both very much $\endgroup$ – Adam Oct 13 '18 at 19:27

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