2018-32.md

course	course_year	question_number	tags	title	year
Groups, Rings and Modules	IB	32	IB 2018 Groups, Rings and Modules	Paper 1, Section II, G	2018

(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 $G \cong A_{4}$.