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

Prove that a group of order 120 is not simple.

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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 + 5kâ”‚24,

then k = 0 , 1

If k = 0, then then Sylow 5-subgroup is normal in G.

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#### Solution Summary

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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