Mathematics Tripos Papers

  • Part IA
  • Part IB
  • Part II
  • FAQ

B1.3

Groups, Rings and Fields | Part II, 2002

State Sylow's Theorems. Prove the existence part of Sylow's Theorems.

Show that any group of order 33 is cyclic.

Show that a group of order p2qp^{2} qp2q, where ppp and qqq are distinct primes, is not simple. Is it always abelian? Give a proof or a counterexample.

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