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3 years ago

Prove that Zn Zn is notisomorphic to any subgroup of Zm for any m.

Mathematics

1 answer:

WINSTONCH [101]3 years ago

5 0

Answer and Step-by-step explanation:

Every group homomorphism ϕ:Zn→Zm extends in a unique way to a linear transformation T:Qn→Qm of vector spaces over Q.

Moreover, ϕ is injective iff T is injective. But T being injective implies n≤m.

Applying this to both ϕ and ϕ−1, we conclude that n≤m≤n.

NOTE:

The proof and step-by-step explanation is in the attachment below

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3 years ago

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