Anku posted an Question
November 12, 2021 • 21:40 pm 30 points
  • IIT JAM
  • Mathematics (MA)

Pls tell mistake in my explanation for option d..i have attached my explanation

pls tell mistake in my explanation for option d. . . .. .. . . . . . . . . . . . . . . . . . . .

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  • Anonymous User Best Answer

    G is not abelian bcoz N. M≠M.N so G/Z is not abelian therefore G/Z is isomorphic to S3

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    but if G/Z will be isomorphic to s3 then G/Z becomes cyclic so by theorem G must be abelian which is contradiction as G is non abelian . so how can it be isomorphic to S3

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    i am using this theorem

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    .s3 is not abelain

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    G/Z and S3 both non abelain

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    but s3 is cyclic and G is non cyclic

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    no s3 is no cyclic

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    S3 is set of all permutations

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    ok got it now..i was having false concept that s3 is cyclic

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