Let order of a group be $108$. Show that there exist a normal subgroup of order $27$ or $9$.
Can we solve without sylow's throrems ? And by sylow's..i need both methods. Thanks
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If $G$ acts on the set of four (or on3) Sylow $3$-subgroups, what can you say about the kernel of the action? – Jyrki Lahtonen Dec 24 '19 at 11:14
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got your point. Thanks sir. – Saimo Dec 24 '19 at 11:31
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I cannot think of a way without Sylow theory :-( – Jyrki Lahtonen Dec 24 '19 at 11:32
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yes, same prob sir , without sylow ,i also dint get solution yet. – Saimo Dec 24 '19 at 11:34