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 =)