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Question: 4 i state sylows theorems ii suppose g is a...

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4. (i) State Sylows theorems. ii) Suppose G is a group with IGI pr where p, q and r are distinct primes. Let np, nq and n, denote, respectively, the number of Sylow p, and r-subgroups of G. Show that Hence prove that G is not a simple group. (iii) Prove that a group of order 980 cannot be a simple group.

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