Mathematics Tripos Papers

  • Part IA
  • Part IB
  • Part II
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Paper 4, Section I, 2E2 E2E

Groups, Rings and Modules | Part IB, 2017

Let GGG be a non-trivial finite ppp-group and let Z(G)Z(G)Z(G) be its centre. Show that ∣Z(G)∣>1|Z(G)|>1∣Z(G)∣>1. Show that if ∣G∣=p3|G|=p^{3}∣G∣=p3 and if GGG is not abelian, then ∣Z(G)∣=p|Z(G)|=p∣Z(G)∣=p.

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