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Deepak Patra posted an Question
November 24, 2021 • 04:36 am 30 points
  • IIT JAM
  • Mathematics (MA)

50. prove that a, has a subgroup of order 12. 51. prove that a, has no subgroup of order 30.

50. Prove that A, has a subgroup of order 12. 51. Prove that A, has no subgroup of order 30.

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    Kanika goswami 1 best-answer

    Such a subgroup would have index 2 and so immediately be normal and non-trivial. But A5 is simple having no non trivial normal subgroup. Implies that A5 has no subgroup of order 30.

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    then what are the subgroup of A5??

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    Total subgroups of A5 are 59 in which 12th order subgroup also.

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    Deepak are you understood?

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