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Homework Statement
Show that the 5-Sylow subgroups of a group of order 90 is normal.
Homework Equations
None.
The Attempt at a Solution
I know that the number [itex]\nu_5[/itex] of 5-Sylow subgroups must divide 90 and be congruent to 1 mod 5. That means that [itex]\nu_5\in\{1,6\}[/itex]. I also know that p-Sylow subgroups are normal iff they are unique, so it seems fairly obvious that I need to try to rule out [itex]\nu_5=6[/itex]. I'm just not sure of how to do it. Can someone give me a nudge in the right direction?