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# Prove that a group of order 120 is not simple.

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Prove that a group of order 120 is not simple.

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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.

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Posting 31061
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.
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• BSc, Manipur University
• MSc, Kanpur University
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