Prove that a group of order 120 is not simple.© BrainMass Inc. brainmass.com December 24, 2021, 5:08 pm ad1c9bdddf
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Prove that a group of order 120 is not simple.
Solution :- 120 = 23.3.5 Let G be a group of order 120.
The number of Sylow 5-subgroup in G is 1 + 5k and 1 + 5k│24,
then k = 0 , 1
If k = 0, then then Sylow 5-subgroup is normal in G.
This solution is comprised of a detailed explanation to prove that a group of order 120 is not simple. It contains step-by-step explanation for the problem by using the theory of Sylow subgroups. Solution contains detailed step-by-step explanation.