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Prabhupada Asked a Question
April 16, 2020 7:47 pmpts 30 pts
  • IIT JAM
  • Mathematics (MA)

Let h and k are two subgroup of g. if h is normal subgroup of k and k is normal subgroup of g, then does it imply that h is normal subgroup of g?

Let H and K are two subgroup of G. If H is normal subgroup of K and K is normal subgroup of G, then Does it imply that H is normal subgroup of G?
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  • Lov kumar
    ANSWER:- YES
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  • Lov kumar
    ANSWER:- Yes
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  • Arzoo Best Answer
    No, It is not true in general. counterexample G=A4 k is normal subgroup of V4 and v4 is normal to A4 but k is not normal to A4
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    Arzoo
    Here k={ (1), (12)(34)} and v4={ (1),(12)(34),(13)(24),(14)(23)} and A4 is alternating group.