IIT JAM
Pooja raghav Asked a Question
July 25, 2020 4:07 pmpts 50 pts
  • IIT JAM
  • Mathematics (MA)

Prove or disprove that if gis a finite abelian group of order n, and k is a positive integer which divides n, then g has at most one subgroup of order k.

Prove or disprove that if Gis a finite abelian group of order n, and k is a positive integer which divides n, then G has at most one subgroup of order k.
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  • Deepak singh Best Answer
    take G = K4 kliens group , it's not true..
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  • Deepak singh thankyou
    see attached
    • cropped-1019306638.jpg
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  • Shashi ranjan sinha thankyou
    There are lots of example to disprove the statement. 1)Order 2 subgroups of dihedral group of order 2n. 2) Quaternion groups, etc.
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