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Part of 2007 IMS

Problems(1)

Group with exactly n subgroups of index 2

Source: IMS 2007

5/12/2007
Suppose there exists a group with exactly nn subgroups of index 2. Prove that there exists a finite abelian group GG that has exactly nn subgroups of index 2.
group theoryabstract algebrasuperior algebrasuperior algebra unsolved