Paper 1, Section II, G

(a) State Sylow's theorems.

(b) Prove Sylow's first theorem.

(c) Let $G$ be a group of order 12. Prove that either $G$ has a unique Sylow 3-subgroup or $G \cong A_{4}$.

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Paper 1, Section II, G

(a) State Sylow's theorems.

(b) Prove Sylow's first theorem.

(c) Let $G$ be a group of order 12. Prove that either $G$ has a unique Sylow 3-subgroup or $G \cong A_{4}$.