Is it necessary for every subgroup of a group to have an Index 2 with respect to the group for the the subgroup to be normal?
is index of normal subgroups of a group always 2?
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group-theory
1 Answers
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No. For example, all subgroups of an Abelian group are normal, and they need not have index 2. On the other hand, all subgroups of index 2 are normal.