Mathematics Tripos Papers

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Paper 4, Section I, 2G2 G2G

Groups, Rings and Modules | Part IB, 2013

Let ppp be a prime number, and GGG be a non-trivial finite group whose order is a power of ppp. Show that the size of every conjugacy class in GGG is a power of ppp. Deduce that the centre ZZZ of GGG has order at least ppp.

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