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Ajay Asked a Question
February 9, 2021 9:28 ampts 30 pts
  • IIT JAM
  • Mathematics (MA)

For a finite abelian group g of order n, is it true that g has a subgroup of order m for each divisor of n? please prove with examples

For a finite abelian group G of order n, is it true that G has a subgroup of order m for each divisor m of n (where m is not necessarily prime)? Please prove with examples
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  • Alka gupta thankyou
    this statement is not ture for finite abelian group it is ture for finite cyclic group. " Lagrange's theorem" states that " The order of every subgroup of a finite group G is a di...
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    Ajay
    But isn't every cyclic group abelian as well?