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GroupTheory - Nanyang Technological University
www1.spms.ntu.edu.sg8 CHAPTER1. GROUPTHEORY 3. x,y∈ Himplies xy−1 ∈ Hfor all x,y. Proof. We prove that 1.⇒ 3.⇒ 2.⇒ 1. 1.⇒ 3. This part is clear from the definition of subgroup.