Mathematics Tripos Papers

  • Part IA
  • Part IB
  • Part II
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A1.4 B1.3

Groups, Rings and Fields | Part II, 2001

(i) Define the notion of a Sylow ppp-subgroup of a finite group GGG, and state a theorem concerning the number of them and the relation between them.

(ii) Show that any group of order 30 has a non-trivial normal subgroup. Is it true that every group of order 30 is commutative?

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