Paper 3, Section I, D

State and prove Lagrange's theorem. Give an example to show that an integer $k$ may divide the order of a group $G$ without there being a subgroup of order $k$.

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Paper 3, Section I, D

State and prove Lagrange's theorem. Give an example to show that an integer $k$ may divide the order of a group $G$ without there being a subgroup of order $k$.