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I can't seem to understand what I should do here... All I did so far is proving that $G$, (such a group), is not simple. But there are many cases, I can't really tell what $n_2,n_3$ and $n_5$ are, only that each of them is either $1$ proving $G$ is normal, or they are really big, forcing the two others to be $1$. I would appreciate your reply.

Donna
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  • I a group of order $30$ they can hardly be "really big". In fact $n_5=n_3=1$. See http://math.stackexchange.com/questions/179830 I don't find the question very clear. What is a "quotient group of a composition series"? – Derek Holt Jan 26 '15 at 09:49
  • @DerekHolt I think the OP is talking about the composition factors of a composition series. Perhaps the OP is asking the determine such composition factors. – Pedro Jan 26 '15 at 14:43
  • I think the OP ought to be able to explain the terminology in the question. Why not just say composition factors if that is what is meant? – Derek Holt Jan 26 '15 at 16:02
  • The OP quoted in these exact words a question taken from an exam. If the OP had understood exactly what he was looking for, he would have not perhaps be asking this question... – Donna Jan 26 '15 at 22:27

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