Paper 3, Section II, D

Groups | Part IA, 2010

State Lagrange's theorem. Let pp be a prime number. Prove that every group of order pp is cyclic. Prove that every abelian group of order p2p^{2} is isomorphic to either Cp×CpC_{p} \times C_{p} or Cp2C_{p^{2} \text {. }}

Show that D12D_{12}, the dihedral group of order 12 , is not isomorphic to the alternating groupA4\operatorname{group} A_{4}.

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