## In a Group S, ab!=ba, choose the possible relationship?

Forum for the GRE subject test in mathematics.
26186514
Posts: 24
Joined: Sat Sep 22, 2012 4:34 pm

### In a Group S, ab!=ba, choose the possible relationship?

A. \$\$a^2=b^2\$\$
B.aba=1

vonLipwig
Posts: 52
Joined: Sat Mar 17, 2012 9:58 am

### Re: In a Group S, ab!=ba, choose the possible relationship?

To investigate whether the first one is possible, think of some small groups and try and find a and b with a^2 = b^2 and ab =/= ba.

For the second, manipulate the equation aba = 1 and see what happens.

26186514
Posts: 24
Joined: Sat Sep 22, 2012 4:34 pm

### Re: In a Group S, ab!=ba, choose the possible relationship?

Oh thanks! I see the second one now.
vonLipwig wrote:To investigate whether the first one is possible, think of some small groups and try and find a and b with a^2 = b^2 and ab =/= ba.

For the second, manipulate the equation aba = 1 and see what happens.

vonLipwig
Posts: 52
Joined: Sat Mar 17, 2012 9:58 am

### Re: In a Group S, ab!=ba, choose the possible relationship?

Excellent. What did you get?

For the first one, try the symmetric group S_3.

26186514
Posts: 24
Joined: Sat Sep 22, 2012 4:34 pm

### Re: In a Group S, ab!=ba, choose the possible relationship?

yes. Coz ab=ab(aba)=(aba)ba=ba if aba=1
and S3 is a brilliant idea! thanks!

vonLipwig
Posts: 52
Joined: Sat Mar 17, 2012 9:58 am

### Re: In a Group S, ab!=ba, choose the possible relationship?

Yep! Good work =)