Paper 3, Section I, E

Groups | Part IA, 2012

State Lagrange's Theorem. Deduce that if GG is a finite group of order nn, then the order of every element of GG is a divisor of nn.

Let GG be a group such that, for every gG,g2=eg \in G, g^{2}=e. Show that GG is abelian. Give an example of a non-abelian group in which every element gg satisfies g4=eg^{4}=e.

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