# Abstract Algrbra : Subgroups and Quotients

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1. Let G be a group and H be a subgroup of G of index equal to 2. Prove that H G

2. Let (G,?) be a group and H G. Prove that if G/H is a p-group and is a p-group then is a p-group H.

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Groups and p-groups are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.

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1. Suppose is a group and is a subgroup of with index 2. Show that .

Proof:

For any ...

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