A. $$a^2=b^2$$

B.aba=1

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

### 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.

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

### 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.

### 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.

For the first one, try the symmetric group S_3.

### 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!

and S3 is a brilliant idea! thanks!

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

Yep! Good work =)