Nidhila Rani Vs posted an Question
September 14, 2020 • 22:02 pm 30 points
  • CSIR NET
  • Mathematical Sciences

A4 has no subgroup of order 6

A4 has no subgroup of order 6 How to prove it? Why it is taking number of 3- cycles to prove this?

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  • Shashi ranjan sinha Best Answer

    If there exist a subgroup of order 6 in A4, then we have shown by the proof 1 that it would must contain all 3-cycles in that group, which is absurd because we have total 8 elements of order 3 in A4 and they can't be all contained in a subgroup of order 6.

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