Let G be a finite group and let n be a divisor of |G|. Show that if H is the only subgroup of G of order n, then H must be normal in G.

I need to show gh^g-1 is in H.

We have |G|=nb since n is a divisor.

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- December 2nd 2010, 09:08 AMkathrynmathfinite groups, normal subgroups, divisors
Let G be a finite group and let n be a divisor of |G|. Show that if H is the only subgroup of G of order n, then H must be normal in G.

I need to show gh^g-1 is in H.

We have |G|=nb since n is a divisor. - December 2nd 2010, 10:48 AMDrexel28
- December 2nd 2010, 03:02 PMkathrynmath
I'm confused. I've never heard the word automorphism

- December 2nd 2010, 05:22 PMDrexel28
- December 2nd 2010, 05:58 PMkathrynmath