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Every subgroup of an abelian group is :
  • a)
    Normal
  • b)
    Cyclic
  • c)
    Quotient
  • d)
    Factor
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Every subgroup of an abelian group is :a)Normalb)Cyclicc)Quotientd)Fac...
Let G be an abelian group and H a sub group of G x be any element G and h any element of H. We have
= eh(∵ G is abelian x-1 h = hx-1)
thus x∈G, x∈G, ⇒ xhx-1 ∈ H
Hence H is normal in G
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Every subgroup of an abelian group is :a)Normalb)Cyclicc)Quotientd)FactorCorrect answer is option 'A'. Can you explain this answer?
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