Anku posted an Question
October 29, 2021 • 09:43 am 30 points
  • IIT JAM
  • Mathematics (MA)

How to solve pls once show steps..

how to solve pls once show steps.. .. . . .. . . . . . .. . . . . . . . . .. . . . . . . . . . .. . . . . . .

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    Navdeep goyal 1 Best Answer

    options C Since 5 is smallest prime divides order of group. And therefore any subgroup of Gof index 5 is Normal. and hence subgroup of index 5 is normal. 5|45 but 5² not | 45 and therefore from sylow theorem ∃ a subgroup of G of order 5. Number of such subgroups will be of 1+5k type and (1+5k) | 9 ⟹k=0 and hence ∃ unique subgroup of G of order 5, and hence it would be normal

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    sir how to check if HK is normal or not i.e. option 1

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    if H and K are normal subgroup of G then HK is also normal sub group of G

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    HK is also normal

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