Can anyone help with the following?

Prove that G cannot have a subgroup H with the order of H=n-1, where the order of G=n, and n is greater than 2.

Thanks!

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- Mar 3rd 2010, 05:26 AMmarchesabstract algebra proof
Can anyone help with the following?

Prove that G cannot have a subgroup H with the order of H=n-1, where the order of G=n, and n is greater than 2.

Thanks! - Mar 3rd 2010, 05:53 AMtonio
- Mar 3rd 2010, 06:34 AMmarches
Thanks, but can't use Lagrange's...not to mention, G and H are infinite--I think Lagrange applies to finite groups. Any other suggestions?

- Mar 3rd 2010, 07:17 AMtonio
- Mar 3rd 2010, 07:27 AMmarches
oops--Right,right, I was thinking the n>2 thing was implying infinite order. But still, we were told not to use Lagrange's. Any other ideas?

- Mar 3rd 2010, 08:23 AMDrexel28