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All subgroups are normal

Source: IMS 2009

May 20, 2009
group theoryabstract algebrasuperior algebrasuperior algebra unsolved

Problem Statement

G G is a group. Prove that the following are equivalent: 1. All subgroups of G G are normal. 2. For all a,bāˆˆG a,b\in G there is an integer m m such that (ab)^m\equal{}ba.
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